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Current seminar

Probability Seminars 2000-2010


Course number: 15-MATH-924-001

Probability Seminar Spring 2010

Time: Mondays 2-3
Place: Seminar room (Old Chem 807)
    Tentative schedule:
  1. March 29:
    • Semester conversion: course syllabi
    • Magda Peligrad, Fourier transforms of stationary processes(joint work with Wei-Biao Wu)
  2. April 5: Wlodek Bryc, UC Adaptive Math Placement Exam | access page | Working notes |
  3. April 12: no seminar Ando's advanced exam will be held in room 623 Old Chem. (2-4PM)
  4. April 19 Room 623: Albert Cohen, Michigan State A Stochastic Approach To Coarsening In Grain Networks [supported by NSF DMS 0830579]
    Many of the high tech devices we use today possess components that are made from polycrystalline materials. From interconnects in microprocessors with higher conductivity to materials that resist fracture, the engineering of these microstructures is crucial to our technological advancement. These macroscopic properties are affected by mesoscale characteristics like grain size, texture, and arrangement of the grains in their topological network of boundaries. A crucial problem in understanding this area of materials science is the modeling and simulation of the evolution of these networks. Simulation of these large, metastable networks involves solution of an average of 50,000 nonlinear partial differential equations. This approach to microstructural evolution can be replaced at a larger scale by a system of master equations for the evolution of grain size distribution functions. An earlier known phenomenological system of this type can be found in the paper of Fradkov et al [1]. Modeling of these equations, however, must be based on accommodating critical events into the deterministic rules for grain growth in order to obtain network properties. Such a model should be built empirically, from large scale simulation. And it must reproduce statistics of the simulation.These properties are the foundation of the master equations proposed by the authors BKLT [2]. In their work, they propose a system of equations that is internally consistent, and suggest that the reassignment of sides from deleted grains is random in nature.

    In the work we present in this seminar, we will show that these master equations do in fact have a consistent probabilistic interpretation. It follows that the empirical equations posed by BKLT have a life of their own as the 'upscale' equations of a stochastic process that describes the coarsening of the grain network . Finally, we show that the existence theory for solutions to these highly nonlinear integro-partial differential equations is symbiotically coupled to an existence theory for this stochastic process.

    • [1] V.E. Fradkov and D. Udler, Two-dimensional normal grain growth: topological aspects, Adv. Physics 43, 739 (1994)
    • [2] K. Barmak, D. Kinderlehrer, I. Livshits and S. Ta'asan, Remarks on a Multiscale Approach to Grain Growth in Polycrystals, Progress in Nonlinear Differential Equations and Their Applications, 68 (2006), pp.1-11.
  5. Thursday, April 22 4:00pm in 309 Braunstein: Aimo Hinkkanen (University of Illinois Urbana-Champaign) Martingales and rotations
    We discuss a class of complex-valued functions in the plane whose complex partial derivatives can be multiplied by functions of unit modulus such that these rotated derivatives then are the end results of two martingales that are martingale transforms of each other. The motivation is that whenever this can be done, known inequalities for martingale transforms due to Burkholder then imply inequalities for various quantities associated with the partial derivatives, including their p-norms. The question originally arose from an attempt to verify a still open conjecture concerning the p-norm of the Beurling-Ahlfors transformation.

    Standard approximation results show that to get such inequalities, it suffices to consider continuous piecewise affine mappings of compact support. The problem becomes how to construct martingales by "combining" affine maps into new ones. We present a proposed algorithm for doing this and describe cases where this algorithm can be carried out to the end to achieve the desired result. The question of whether the algorithm always works remains open. An affirmative answer to this would imply affirmative answers to a number of open conjectures.

  6. April 26: Florence Merlevede [partially supported by NSF DMS 0830579] Room 623 Almost sure invariance principles for stationary weakly dependent sequences
    In this talk, we give precise rates of convergence in the strong invariance principle for the partial sums associated to a class of weakly dependent sequences included strong mixing sequences. We shall give the ideas of proofs which are based on an explicit construction of the approximating sequence of iid Gaussian random variables with the help of conditional quantile transformations. This talk is based on a joint work with E. Rio.

  7. May 3 (seminar room): Sunder Sethuraman, Iowa State, On occupation times in simple exclusion process [This talk is supported by NSF conference grant DMS 0830579]
  8. May 5 Colloquium at 4PM, Room Chem 623 325 Braunstein: Wojbor A.Woyczynski , Department of Statistics and Center for Stochastic and Chaotic Processes in Sciences and Technology, Case Western Reserve University Competition between nonlinear and stochastic long -range effects in evolution equations [This talk is supported by NSF conference grant DMS 0830579]
    The classical parabolic nonlinear evolution equations such as Burgers, and Navier-Stokes equations have, in a sense, balanced influence of the quadratic nonlinearity and the Brownian Motion, local diffusion over the long-time shape of the solutions. This balance can be destroyed if one considers other nonlinearities and nonlocal diffusion, including those related to the Levy processes which feature long-range jumps. The issue will be discussed in the case of the so-called fractional conservation laws. Interacting particle systems approximations for such evolution problems, with numerical implications, will also be presented.

  9. May 10, 2PM, in 325 Braunstein: Jack Silverstein, NC State Eigenvalues of Large Dimensional Random Matrices Abstr (PDF) [This talk is supported by NSF conference grant DMS 0830579]
  10. May 17: (no seminar)
  11. May 24 (Seminar Room): Arup Bose, Indian Statist Inst, Patterned matrices and various notions of independence. This is joint work with Rajat Subhra Hazra and Koushik Saha. [The talk is supported by Taft]

Course number: 15-MATH-925-001

Probability Seminar Winter 2010

Time: Mondays 2-3
Place: 616D Rieveschl and Seminar room (Old Chem 807)
  1. Monday, Jan 11: Virgil Pierce, The Pfaff lattice equations and the symplectic eigenvalue problem
    The QR-algorithm is a standard method of diagonalizing a matrix. It has an intimate relationship with the Toda lattice equations (a classic example of a coupled system of nonlinear differential equations). Integer evaluations of a Toda lattice evolution with a non-standard choice of Hamiltonian give the iterates of the QR-algorithm.

    The SR-algorithm is a generalization of the QR-algorithm which computes the eigenvalues of a symplectic matrix while preserving the symplectic form of the matrix. We will show that this algorithm is equivalent to a member of the Pfaff lattice hierarchy. The Pfaff lattice hierarchy was introduced by Adler and van Moerbeke to describe the partition functions of GOE and GSE random matrices. This lattice is presented as a system of evolution equations on a matrix variable and is based on the SR-factorization. We will show that the even members of Pfaff lattice hierarchy give alternative algorithms for diagonalizing a symplectic matrix which preserve the symplectic form of the matrix.

    This is joint work with Yuji Kodama.

  2. Colloquium, Tue Jan 12, 4-5PM in 309 Braunstein Hall: Robert Buckingham Asymptotic analysis of the semiclassical sine-Gordon equation
    The small dispersion or semiclassical limit of the sine-Gordon equation models magnetic flux propagation in long Josephson junctions. In principle, any well-posed initial-value problem for the sine-Gordon equation can be solved using the inverse-scattering transform. However, in practice the solution can be computed explicitly for only a handful of initial conditions. We first present a recent spectral confinement result, giving conditions when the spectrum of the system must lie in certain regions. Secondly, we discuss ongoing work on the asymptotic behavior of general soliton ensembles in the semiclassical limit. Parts of this work are joint with Peter Miller.
  3. Jan 25: no seminar
  4. Feb 1 Chem 807: Magda Peligrad Self-normalized CLT for linear processes based on joint work with Hailin Sang
  5. Feb 8 (816 Swift): Convexity and convergence results for backward stochastic differential equations Christoph Frei, Centre de Mathématiques Appliqué, École Polytechniqu, Paris, France
  6. Feb 15: No seminar - semester conversion discussion
  7. Feb 22: Semester conversion (?)
  8. March 1: Wlodek Bryc Meixner Esnembles, based on joint work in progress with Gerard Letac.
  9. March 8: Magda Peligrad, The role of averaging in Invariance principles

Course number: 15-MATH-924-001

Probability Seminar Autumn 2009

Time: Mondays, 2-3
Place: Seminar Room
Picture: TBP
  1. Sept 28: Organizational meeting
  2. Oct 5: Wlodek Bryc, Markov processes with Marchenko-Pastur laws
  3. Th, Oct 8 4PM, David Mason, University of Delaware, Old and new research on the student t-statistics
  4. Oct: 12: Robert Buckingham, Random Hermitian matrices with a small-rank external source
  5. Oct 19: Robert Buckingham (continued)
  6. Oct 26: Magda Peligrad, CLT for reversible Markov Chains
  7. Nov 2: Magda Peligrad (cont)
  8. Nov 6 (Friday): time 2-3 Room: Braunstein 316. Speaker: Mark Meckes, Case Western Reserve. Title: Concentration of noncommutative polynomials of random matrices
  9. Nov 9: No seminar
  10. Nov 16: Tamer Oraby (U. Ottawa)
  11. Nov 23: Sunder Sethuraman, Iowa State Intro to some forms of data clustering
  12. Nov 30: Ando Central Limit Theorem for Generalized Binomial Distribution

Course number: 15 MATH 927

Taft Research Seminar on Probability Theory and Applications

Spring 2009 Visiting Fellow: Wei Biao Wu, U. Chicago

Time: mostly We 4-5
Place: announced in emails each week!!!
  1. Th, April 2, 4-5, Room 309 Braunstein: Colloquium by Mihai Popa, Indiana U, Bloomington Combinatorics of some non-commutative types of independence
    Free probability is maybe the most popular part of non-commutative probability theory. This young field, at the intersection of probability theory, operator algebra, complex analysis and combinatorics is also connected to other sciences, from physics to psychology and engineering. But freeness is not the only notion of non-commutative independence. Under certain universality assumptions one gets 2,3, or 4 types of independence and various interpolation models. In this talk I will give an introduction to non-commutative probability , some of its specific techniques and problems it has tackled I will emphasize the combinatorial part, where root systems, partitions, crossings, embracings, planar and rooted trees aggregate in an effective machinery.
  2. Fri, April 3, 3-4, Braunstein 312: Wei Biao Wu Simultaneous Confidence Bands in Time Series
    I will talk about statistical inference of trends in mean non-stationary models, and mean regression and conditional variance (or volatility) functions in nonlinear stochastic regression models. Simultaneous confidence bands are constructed and the coverage probabilities are shown to be asymptotically correct. The Simultaneous confidence bands are useful for model specification problems in nonlinear time series. The results are applied to environmental and financial time series.
  3. We, April 8: COVARIANCE MATRICES ESTIMATION FOR STATIONARY PROCESSES by Wei Biao Wu
    I will discuss estimation of covariance matrices of stationary processes. Under a short-range dependence condition for a wide class of nonlinear processes, I will show that the banded covariance matrix estimates converge in operator norm to the true covariance matrix with explicit rates of convergence. I will also consider the consistency of the estimate of the inverse covariance matrix. These results are applied to a prediction problem, and error bounds for the finite predictor coefficients are obtained. The work is joint with Mohsen Pourahmadi of TAMU.
  4. We, April 15: no seminar
  5. We, April 22: Colloquium Rm 325 Braunstein Hall Tuomo Kuusi, Columbia University and Helsinki University of Technology, Harnack inequalities for solutions to partial differential equations
    Harnack inequalities describe, in quantitative ways, behavior of solutions to partial differential equations. These inequalities were originally defined for harmonic functions in the plane and much later became an important tool in the theory of harmonic functions and, more generally, partial differential equations. The purpose of my talk is to explain major ideas behind Harnack inequalities in different cases. The emphasis is in the qualitative behavior of solutions. Moreover, I will introduce a few consequences that may be deduced from Harnack inequalities, motivating the study of them. They are both deep and powerful. The understanding of Harnack inequalities for solutions to a general class of nonlinear parabolic PDEs has risen significantly recently. I will explain the history of the problem, reviewing fundamental works of De Giorgi and Moser in the linear case, and then introducing new results for a general class of equations with degenerate structure. I will also very briefly introduce main techniques to prove Harnack inequalities in different cases.
  6. Barnett Lecture Thursday April 23rd, from 3:00pm to 4:00pm in 800 Swift Hall. The speaker is Professor Stephen Semmes, the Noah Harding Professor of Mathematics at Rice University. The title of the talk is Happy Fractals
  7. Friday April 24 in 807 Old Chem.(Seminar Room) Time 3:00-4:00 Speaker: Dalibor Volny University of Rouen, France Topic: Limit theorems via martingale approximation
  8. We, April 29: Wei Biao Wu, University of Chicago Moderate Deviations in room 806
    Abstract: I will present an asymptotic expansion for probabilities of moderate deviations for iid random variables and for stationary processes. The sharpness of moment conditions will be discussed. The dependence measures are easily verifiable (cf W. B. Wu (2005), Nonlinear system theory: Another look at dependence. Proc Natl Acad Sci USA. 102)
  9. We, May 6: Wlodek Bryc Frobenius-Harper technique for proving asymptotic normality in some recurrences based on a 1999 paper of Di Warren. (see also her proofs supplement)
  10. Friday May 8 (Seminar Room) Time 3:00-4:00: Wei-Biao Wu Fourier and wavelet transforms of stationary processes
    I will discuss Fourier and wavelet transforms of stationary, causal processes. Under mild conditions, Fourier transforms are shown to be asymptotically independent complex Gaussian at different frequencies. To this end, I will apply Carleson's Theorem, a very deep result in harmonic analysis.
  11. We, May 13, Room 325 Braunstein Hall: Hailin Sang University of Cincinnati Variable bandwidth kernel density estimation with clipping procedures
    It is shown that the McKay (1993) and Jones, McKay and Hu (1994) modifications of Abramson's (1982) variable bandwidth kernel density estimator satisfies optimal asymptotic properties for estimating densities with four or six uniformly continuous derivatives, uniformly on bounded sets where the preliminary estimator of the density is bounded away from zero.
  12. We, May 20: Wei Biao Wu, University of Chicago Moderate Deviations Part 2
    Abstract: I will present an asymptotic expansion for probabilities of moderate deviations for iid random The sharpness of moment conditions will be discussed. The dependence measures are easily verifiable (cf W. B. Wu (2005), Nonlinear system theory: Another look at dependence. Proc Natl Acad Sci USA. 102)
  13. We, May 27 (Braunstein 325): Arup Bose, (Indian Statistical Institute Kolkata) Limiting Spectral Distribution of large dimensional circulant type matrices with dependent inputs.
  14. We, June 3:

Cincinnati Symposium on Probability Theory and Applications 2009 links: IMS IMA Probability Seminar Probability Web Conference Service Mandl

Winter 2009 Visiting Fellow: Mikhail Gordin of Steklov Institute of Mathematics at Saint Petersburg (POMI)

Time: Wednesdays, 4:15-5:00
Place: Seminar Room 807
  1. Tu, Jan 20 Room Swift 800, 2 - 3 pm: Qingshuo Song, University of Southern California A Class of Impulse Control problems and Related Quasi-Variational Inequalities
  2. We, Jan 21, Braunstein 325, 4 - 5 pm: Tao Mei, Univ. of Illinois Urbana-Champaign TBA
  3. Fri, Jan 23 10AM-11 Room 309 Zimmer Hall: Magda Peligrad, Bernstein-type inequalities
  4. Th, Jan 29, Braunstein 325, 4 - 5 pm: Robert Buckingham, U. Montreal, New Formulas for Tracy-Widom Functions
    The Tracy-Widom functions describe the limiting distribution of a variety of statistical quantities, including the largest eigenvalue of a random matrix drawn from the Gaussian orthogonal, symplectic, or unitary ensembles (GOE, GSE, or GUE), the longest increasing subsequence of a random permutation, and the outermost particle in a sea of non-intersecting Brownian particles. We obtain new formulas for the Tracy-Widom functions in terms of integrals of Painleve functions. Using these new formulas we find the complete asymptotic expansion of the left-hand tail of the GOE and GSE Tracy-Widom functions for the first time, as well as a second proof of the recently obtained result for the GUE case. We conclude by discussing progress on a new family of "incomplete" Tracy-Widom distributions corresponding to the largest observed eigenvalue if each eigenvalue has a fixed probability of being observed. This is joint work with Jinho Baik and Jeffery DiFranco.
  5. Fri, Jan 30 10AM, Zimmer 309: Magda Peligrad, Limit theorem via martingale approximations
  6. Mo, Feb 2:, 1PM-2 Room 719 Swift: Miriana Vuletic, Caltech Asymptotics of large random strict plane partitions and generalized MacMahon's formula
    We introduce a measure on strict plane partitions that is an analog of the uniform measure on plane partitions. We describe this measure in terms of a Pfaffian point process and compute its bulk limit when partitions become large.

    The above measure is a special case of the shifted Schur process, which generalizes the shifted Schur measure introduced by Tracy and Widom and is an analog of the Schur process introduced by Okounkov and Reshetikhin. We use the Fock space formalism to prove that the shifted Schur process is a Pfaffian point process and calculate its correlation kernel.

    We also obtain a generalization of MacMahon's formula for the generating function of plane partitions. We give a 2-parameter generalization related to Macdonald's symmetric functions. The formula is especially simple in the Hall-Littlewood case.

  7. We, Feb 4 at the regular time 4PM, Seminar Room 807: Mikhail Gordin, Limit theorems via mixing extensions. Applications to toral automorphisms.
    Limit theorems for a hyperbolic or partially hyperbolic dynamical system are usually proved by means of a clever partitioning the phase space of the system. This should lead to the creation of a family of sigma-filelds with customary mixing properties when the machinery of weak dependence is applicable. We are going to consider an alternative approach when no cutting of the phase space is performed. Instead, by means of probabilistic tools an extension of the original dynamical system is constructed supplied with a family of sigma-field enjoying nice mixing properties. We will discuss advantages and drawbacks of this approach and consider ergodic toral automorphisms as examples where this approach goes smoothly and leads to new conclusions.
  8. Fri, Feb 6: Anna Amirdjanova, U. Michigan Nonlinear filtering of random fields in the presence of long-memory noise
    An interesting estimation problem, arising in many dynamical systems, is that of filtering; namely, one wishes to estimate a trajectory of a signal process (which is not observed) from a given path of an observation process, where the latter is a nonlinear functional of the signal plus noise.

    In the classical mathematical framework, the stochastic processes are parameterized by a single parameter (interpreted as ``time''), the observation noise is a martingale (say, a Brownian motion), and the best mean-square estimate of the signal, called the optimal filter, has a number of useful representations and satisfies the well-known Kushner-FKK and Duncan-Mortensen-Zakai stochastic partial differential equations.

    However, there are many applications, arising, for example, in connection with denoising and filtering of images and video-streams, where the parameter space has to be multidimensional. Another level of difficulty is added if the observation noise has a long-memory structure, which leads to nonstandard filtering evolution equations. Each of the two features (multidimensional parameter space and long-memory observation noise) does not permit the use of the classical theory of filtering and the combination of the two has not been previously explored in mathematical literature on stochastic filtering.

    This talk focuses on nonlinear filtering of a signal in the presence of long-memory fractional Gaussian noise. We will start by introducing first the evolution equations and integral representations of the optimal filter in the one-parameter case, when the noise driving the observation is represented by a fractional Brownian motion. Next, using fractional calculus and multiparameter martingale theory, the case of spatial nonlinear filtering of a random field observed in the presence of a persistent fractional Brownian sheet will be explored.

  9. Feb 11: Mikhail Gordin Limit theorems via mixing extensions. Applications to toral automorphisms.(continued)
  10. Feb 18: Mikhail Gordin (continued)
  11. Feb 19, 4-5 (Colloquium): Mikhail Gordin
  12. Feb 25: Wlodek Bryc will summarize results with Wesolowski.
  13. March 4: Jeesen Chen will talk on n Stein's method.
  14. March 11 (last seminar):
  15. March 20-23: Cincinnati Symposium on Probability Theory and Applications

Fall 2008 Visiting Fellow: Jacek Wesolowski of Warsaw University of Technology

Time: Mondays 2-2:50
Place: Seminar Room (Chem 807)
  1. Mo, Sept 29, 2-3: Organizational meeting: who is who, what are our interests, who would like to talk this quarter.
  2. Mo, Oct 6, 2-2:50 (no cookies): Jacek Wesolowski (Warsaw Univ. Techn. Quadratic harnesses
  3. Mo, Oct 13: Sunder Sethuraman (Iowa State University) Large deviations for the leaves in some random trees
  4. Mo, Oct 20: Andoniaina (Ando) Rarivoarimanana Stein method
    • Fri, Oct 24: Midwest Colloquium
  5. Mo, Oct 27 Braunstein 301: Magda Peligrad Moderate deviation for dependent sequences
  6. Mo, Nov 3, 2-2:50 (no cookies): Michael Woodroofe (University of Michigan) Martingale approximations
    • Th, Nov 6, 4-5PM Room 325 Braunstein: Michael Woodroofe (University of Michigan) Isotonic regression
  7. Mo, Nov 10 Braunstein 301: Yu-Juan Jien A stochastic differential equation driven by fractional Brownian motion
    • Tu, Nov 11: Veterans Day (UC is closed)
  8. Mo, Nov 17: Wlodek Bryc, Large Deviations for some Markov chains that arise in random graph models (Continuation of Oct 13 talk. Based on joint paper with D. Minda and S. Sethuraman)
    • November 20-21, 2008, Seventh Northeast Probability Seminar, New York University
  9. Mo, Nov 24 Braunstein 301 : Hailin Sang, Uniform Convergence Rate of Data Driven Kernel Density Estimators.
    • Nov 27-28: Thanksgiving (UC is closed)
  10. Mo, Dec 1, 2-2:50 Braunstein 301: Jacek Wesolowki, ASYMPTOTICS OF GENERALIZED PERMANENTS WITH APPLICATIONS
    Abstract: Permanents of random matrices with iid entries converge to lognormal or normal variables. For generalized permanents the limit is described in terms of the multiple Ito-Wiener integral of elements of Hoeffding decomposition. This theory parallels the one which has been developed for U-statistics. Applications for counting problems for perfect matchings in bi-partite graphs include for instance counting monochromatic matchings or counting matchings with a given color structure of edges. The talk is based on Ch. 5 of a little book "Symmetric Functionals on Random Matrices and Random Matching Problems" (Springer, 2008) co-authored by Grzegorz Rempala and myself.
  11. Fri, Dec 6: Last day of classes

Probability Seminar Spring 2008

Time: Wednesdays, 11-12
Place: Braunstein 326
  1. April 5-6 AMS Meeting #1038, Bloomington
  2. April 9: no seminar
  3. April 10, 4-5: Florence Merlevède, Université Paris 6 Rates of Convergence in the Central Limit Theorem
    This talk will survey some distances between two probability laws and the relations between them. They are used to obtain various rates of convergence in the central limit theorem for sums of independent and dependent random variables.
  4. April 16: no seminar
  5. April 23: no seminar
  6. April 30: Magda Peligrad Ibragimov's conjecture
  7. May 7: Sunder Sethuraman (Iowa State U) Martingale proof of Dobrushin's CLT.
  8. May 14: Wlodek Bryc, Random Toeplitz and other structured matrices>.
  9. May 21: Arup Bose (Indian Statist. Inst.), Limiting Spectral Distribution of Random Matrices.

Probability Seminar Winter 2008

Time: Wednesdays, 1-2
Place: Old chem 804
  1. Jan 24, Th 4-5: Todd Kemp (MIT), Colloquium Talk: Logarithmic Sobolev inequalities: new insights on an important tool
    The logarithmic Sobolev inequality, discovered by L. Gross, is a weak form of a Sobolev inequality: it gives control of a function through average information about its derivatives. It has become a ubiquitous tool in global analysis and probability theory, with important applications in stochastic analysis, large deviations, spectral theory, non-linear PDE, geometric analysis, non-commutative geometry, and more. As a stunning example, the logarithmic Sobolev inequality inspired Perelman's proof of the Poincar\'e conjecture.

    In this talk, I will give an introduction to the area of logarithmic Sobolev inequalities. I will then discuss new insights on such inequalities in the context of regular function spaces, such as holomorphic and subharmonic functions. In recent work with P. Graczyk, J. Loeb, and T. Zak, we have discovered a new and very general logarithmic Sobolev inequality for logarithmically-subharmonic functions. I will discuss these results and give clues about their significance.

  2. Jan 25, Fri, 1-2 Old Chem Room 807: Special Seminar, joint with Geometric Analysis. Speaker: Todd Kemp (MIT), Logarithmic Sobolev inequalities: new insights on an important tool
  3. Jan 30: no seminar
  4. Feb 6: Sunder Sethuraman (Iowa State U): On a locker problem
  5. Feb 13: Wlodek Bryc Wick formula for quaternion-valued Gaussian n-touples. (based on joint work in progress with Virgil Pierce) Notes
  6. Feb 20: Magda Peligrad Exponential martingale approximation for linear process
  7. Feb 27: no seminar
  8. March 5: M. Bhaskara Rao The Krein-Milman Theorem -- a puzzler
  9. March 12: M. Bhaskara Rao (continued)
Spring break: March 24-29


Probability Seminar Autumn 2007

Time: Wednesdays 3-4
Place: Chem 605
  1. Oct 3: no seminar (RPT)
  2. Oct 10: Jeesen Chen, On the probability of a lucky number
  3. Oct 17: Rec center 3210 Tamer Oraby, PhD defense
  4. Oct 24: no seminar
  5. Oct 31: no seminar
  6. Nov 7: no seminar
  7. Nov 14: no seminar
    • Thursday, Nov 15 Colloquium talk by Virgil Pierce, OSU. Recent Results for the Toda and Pfaff Lattice Hierarchies Abstract: Orthogonal and unitary ensembles of random matrices are standard models for statistical and quantum physics. A fundamental object of study is the partition function, which is expressed as an integral over the ensemble of matrices. In the unitary case this function is a tau-function of the Toda lattice hierarchy, meaning it generates solutions of the hierarchy. The Toda lattice is a classical example of an integrable hierarchy and possesses a number of interesting structures. In the orthogonal ensemble case, Adler and van Moerbeke showed that the partition function is a tau-function of the Pfaff lattice hierarchy. Yuji Kodama and I have shown that the Pfaff lattice is an integrable system. I will outline the above relations, show how they are useful for finding explicit solutions of some graphical combinatoric problems and illustrate some recent results for the Pfaff lattices.
  8. Nov 21: no seminar
  9. Nov 28: ~

Stochastic Calculus study group

organized by B. Zhang and T. Oraby will study An Introduction to Stochastic Differential Equations (version 1.2) by L. C. Evans.

Tuesdays 5-7 in the math launge

  • Ch 2, Probability: Tamer (2 weeks)
  • Ch 3, Brownian motion, Hongjun Wang (2 weeks)
  • Ch 4, Stochastic integrals, ... (2 weeks ?)
  • Ch 5, Stochastic diff eqtns ... (2 weeks ?)
  • Ch 6, Applications
... (N-1 weeks)

Probability Seminar Spring 2007

Time: Mondays 2-3
Place: Seminar Room Chem 807
  1. Th, March 28, 4-5 in Braunstein 309, Michael Woodruff (University of Michigan), The Law of the Iterate Logarithm for Stationary Processes
    Abstract: The Law of Large Numbers, the Central Limit Theorem, and the Law of the Iterated Logarithm for independent and identically distributed sequences of random variables are three central, perhaps dominant, results of classical probability theory. The Ergodic Theorem provides a complete extension of the Law of Large Numbers to sequences that are dependent, but stationary. The Central Limit Theorem and Law of the Iterated Logarithm do not extend as completely, but only under additional conditions that effectively limit the amount of dependence. During the past decade there has been some progress on understanding the Central Limit Theorem for stationary processes, resulting in conditions that are sufficient and nearly necessary, at least for the conditional version of the Central Limit Theorem. The talk will present recent efforts to modify the arguments leading to the Central Limit Theorem to obtain a Law of the Iterated Logarithm. It will begin with some background material on the Law of the Iterated Logarithm and a selective review of recent work on the Central Limit Theorem for stationary sequences. It will then describe the modifications necessary to obtain the Law of the Iterated Logarithm.
  2. April 9: no seminar
  3. April 16: no seminar
  4. April 23: Florence Merlevède, Université Paris 6 Rates of convergence for the Wasserstein distances in the central limit theorem for stationary sequences
    Abstract: In this joint work with J. Dedecker and E. Rio, we obtain convergence rates in the central limit theorem for stationary sequences in Lp for Wasserstein distances of order r, for p in ]2,3] and r in ]p-2,p]. The conditions are expressed in terms of projective criteria. The results apply in particular to non-adapted sequences.
  5. Colloquium talk: Thursday, April 26: Wlodek Bryc Classical and noncommutative probability
  6. April 30: M. Bhaskara Rao Patterns in coin tossing
  7. Colloquium on Tue, May 1 at 4PM Sunder Sethuraman Iowa State University On Scaling Limits of a Tagged Particle in Simple Exclusion Particle Systems
    Informally, the simple exclusion process follows a collection of random walks which interact in that they are not allowed to jump onto each other. In this talk, we consider the motion of a distinguished, or tagged, particle in this particle system. We review some of the past results and discuss some new contributions.
  8. May 7: Wlodek Bryc, Moments of real Wishart matrices
  9. May 14:
  10. May 21:
  11. May 28: no seminar (holiday)

Probability Seminar Winter 2007

Time: Mondays 2-3
Place: Seminar room Chem 807
  1. Jan 22: Magda Peligrad, Moderate deviation under projective criteria
  2. Jan 29: Sunder Sethuraman, On the count of certain strings in Bernoulli sequences
  3. Feb 5: Wlodek Bryc Asymptotic normality of traces of polynomials in Wishart matrices
  4. Feb 12: canceled
  5. Feb 19: Tamer Oraby On Shoshnikov's approach to maximal eigenvalue problem
  6. Feb 26: Special Room Swift 620 Tamer Oraby, Practice interview talk.
  7. March 5: Magda Peligrad Processes with negatively associated increments
  8. Thursday, March 15. Time: 4PM Place: Braunstein 309: Roland Speicher, Queens Strong Haagerup inequalities
    In a holomorphic context, some analytic inequalities improve when restricted to a holomorphic subalgebra. We are exploiting this phenomena in a non-commutative situation. Concretely, we show that one can improve Haagerup's classical inequality for norms of convolution operators on the free group if one restricts to operators which involve only the generators (but not their inverses) of the free group. The proof relies on a good understanding of moments of the involved operators and is mainly combinatorial. This is joint work with Todd Kemp.
  9. March 16/17: AMS meeting Miami University, Oxford, OH.

Functional Analysis Seminar

Wednesday 3-4 pm, Feb 21, Feb 28, March 7 Seminar room (OC 807) Victor Kaftal, Majorization theory for infinite sequences
Majorization for finite sequences is linked to doubly stochastic matrices, convexity, the diagonals of selfadjoint matrices (the Schur-Horn Theorem) and more, and so it has been of interest to researchers in several areas of math. Little was know until recently about majorization for infinite sequences but we have now some new results.

Probability Seminar Autumn 2006

Time: Mondays 2-3
Place:Chem 807
  1. Sept 25: Organizational meeting
  2. Oct 2: Wlodek Bryc Complex Wishart matrices
  3. Oct 9: Wlodek Bryc Complex Wishart matrices, continued
  4. Oct 16: Sunder Sethuraman (Iowa State U) On some random graph problems
  5. Oct 19: 4-5 PM Colloquium talk: Dalibor Volny University of Rouen, France

    Martingale approximation of stationary sequences

    In the last few years, important contributions to the study of martingale approximations of stationary processes have been published. I'll have a closer look at the Wu and Woodroofe approximation (Ann. Probab. 2004) and I shall indicate that it can be generalized to non adapted processes. The method easily extends to the CLT of Maxwell and Woodroofe (2004) but not to the invariance principle of Peligrad and Utev (2005); there the non adapted version seems to remain open. Various examples will show that the martingale approximation depends on the choice of the filtration.
  6. Oct 21-22: AMS meeting
  7. Oct 23: no seminar
  8. Oct 30: Magda Peligrad, Inequalities and limit theorems under weak association.
  9. Nov 6: Magda Peligrad, Inequalities and limit theorems under weak association (cont.)
  10. Nov 13: no seminar(?)
  11. Nov 20: Room: Swift 608 Time: 2-3 Pando Georgiev (CS Dept) Independent Component Analysis and a cross-cumulant measure for independence
    We revisit some cumulant methods for Independent Component Analysis - an unsupervised learning method with increasing popularity and applicability in number of disciplines. A rigorous justification of identifiability of the linear ICA method by kurtosis maximization is given by a simple lemma from optimization theory, which gives a basis for a generalization of the famous Fixed Point Algorithm for ICA for high order cumulants. We propose a measure for independence of group of random variables, given by a sum of cross-cumulants of a given order n. Similar measure was known for the case of four order cross-cumulants from the JADE algorithm for ICA. We derive a formula for its calculation using cumulant tensors. In the case n=4 our formula allows efficient calculation of this measure, using cumulant matrices. Much attention is devoted to the case of six order cross-cumulants, aiming to show that this measure can be calculated using again cumulant matrices. We provide a simple proof of the main ICA theorem concerning identifiability of the linear ICA model using the properties of the cross-cumulants instead of the Darmois-Skitovitch theorem from statistics, used for this purpose in the literature on ICA. Various ICA algorithms are demonstrated.
  12. Nov 27: M. Bhaskara Rao A discrete probability problem in chemical bonding

Probability Seminar Spring 2006

Time: Mondays, 11-12
Place: Seminar Room
  1. Apr 3:
    • Organizational meeting
    • Wlodek Bryc: Natural Exponential Families and their free counterpart (Based on joint work with M. Ismail) |Slides|(.4MB)
  2. Apr 10: Magda Peligrad Moderate Deviations
  3. Thu, Apr 13, 4-5PM: Colloquium Talk by Florence Merlevède, Université Paris 6 On the weak invariance principle for non-adapted sequences under projective criteria
    I shall present some results about the central limit theorem and its weak invariance principle for sums of non-adapted stationary sequences, under different normalizations. Our conditions involve the conditional expectation of the variables with respect to the given sigma-algebra, as done in Gordin (1969) and Heyde (1974.) These conditions are well-adapted to a large variety of examples, including linear processes with dependent innovations or regular functions of linear processes.
  4. Apr 17: Tamer Oraby, Free multiplicative convolution
  5. Thu, Apr 20, 4-5PM: Colloquium Talk by Sunder Sethuraman, Iowa State University Diffusivity of a tagged particle in a "zero-range" system of interacting particles
    The "zero-range" system is an (infinite) collection of dependent random walks on Zd which models various types of traffic. Informally, the interaction is in that a particle jumps with a rate depending on the number of particles at its vertex, but to where it jumps is selected independently. In this talk, we consider a distinguished, or "tagged," particle in this system and discuss its asymptotic behavior including some recent diffusive estimates in "equilibrium." In particular cases, we also discuss approximation of the tagged position by a Brownian motion with parameters depending on the form of the interaction and the density of particles.
  6. Apr 24 Room Change:Rec Center 3230: Krzysztof Podgorski, IUPUI, Genomics, microarray analysis and mathematical statistics
  7. May 1 Room Change:Rec Center 3230: M. Bhaskara Rao, One Bulb? Two Bulbs? How many bulbs light up? A problem from a pharmaceutical company
  8. May 8: Wlodek Bryc Quadratic Harnesses
    This is a "practice talk for a conference". The topic is classificiatioon of rpocesses with linear regressions and quadratic conditional variances.
  9. May 15 Room Change:Rec Center 3230: Wojciech Matysiak Random sequences with linear regressions - an operator approach
  10. May 22: Room Change:Rec Center 3230 Tamer Oraby Limiting spectra of random block matrices
  11. May 29: (Memorial Day - no classes)

Probability Seminar Winter 2006

Time: Mondays, 3-4, 4-5
Place: Chem 724

Schedule

  1. Jan 9: no seminar
  2. Jan 16: holiday
  3. Jan 23: Tamer Oraby, The limiting spectra of Girko’s block-matrix
  4. Jan 30: ?
  5. Feb 6: (none)
  6. Feb 13: (none)
  7. Feb 20: posponed?
  8. Feb 27: Magda Peligrad Moderate deviations for martingales
  9. March 6:
  10. March

Related Activities

  1. 6H Mini Course Introduction to Large Deviations (W. Bryc)
    • Tue, Jan 3, 3:30-5:30, Introduction
    • Th, Jan 5, 3:30-5:30, Equivalent Definition, Criteria
    • Th, Jan 12, 3:30-5:30, Ben Arous-Guionnett's Theorem
  2. Feb 4-18: visit by R. Szwarc

Statistics Seminar

Wednesdays 3-4, Room 825

Probability Seminar Fall 2005/06

Schedule

  1. Sept 28: Organizational meeting in Seminar Room
  2. October 5: Tamer Oraby, Limiting spectral distribution of symmetric matrices with weakly dependent entires
  3. October 12: Mourad E.H. Ismail,University of Central Florida Orthogonal Polynomials and Birth and Death Processes
    Abstract We survey the role played by orthogonal polynomials in the analysis of transision probabilities of birth and death processes and associated random walks. Several examples will be mentioned.
    • Th, October 13, 4PM: colloquium Talk Mourad E.H. Ismail,University of Central Florida Orthogonal Polynomial, Discriminants, and Electrostatic Equilibrium Problems
      Abstract Stieltjes and Hilbert computed discriminants of Jacobi polynomials. Stieltjes studied the electrostatics equilibrium problem of n-unit charged particles restricted to (-1,1) under the external field of charges (a+1)/2 and (b+1)/2 at ±1. The potential is a logarithmic potential. Stieljes showed that the equilibrium position of the particle is at the zeros of the Jacobi polynomial Pn(a, b)(x). We discuss the recent developments on this problem, its extension to general orthogonal polynomials and the role discriminants play in the solution of the problem. We also mention the more recent work where similar techniques are used to solve the Bethe Ansatz equations for the XXZ and XXX models.
  4. October 19: Magda Peligrad Asymptotic negative association
  5. October 21: Twenty-Seventh Midwest Probability Colloquium October 21-22, 2005 http://www.math.northwestern.edu/mwp/
  6. October 26: Wlodek Bryc, Some open questions on random matrices Slides(300KB)
  7. Nov 2 Computer Lab: Arup Bose, Indian Statistical Institute Limiting Spectral distribution of random matrices
  8. Nov 9: Wlodek Bryc Exponential Families
  9. Nov 16: Zeynep Teymuroglu Optimal Portfolio Theory
    Abstract We assume that real-world financial markets are partially hedgable, therefore they are fundamentally incomplete [3]. It has been known for some time that there is no unique price for financial contracts in incomplete market. Recently, by the help of reduced Monge-Ampere equations, [1] introduces a new method for pricing and hedging of financial instruments in in/complete market. Financial contracts still have non-unique prices in incomplete setting, but the prices depend on only g, so-called relative risk aversion.
    • [1] S.D. Stojanovic: Higher dimensional fair option pricing and hedging under Hara and Cara utilities. (Preprint, August 2005)
    • [2] S.D. Stojanovic: Pde methods in financial modeling. 25th Annual Searcde in Dayton
    • [3] S.D. Stojanovic: Actuaries vs. Financial Engineers in regard to valuation: the truth is now found to be in between. Garp Risk Review, Sept/Oct 2005
  10. November 18, 2-3:15 pm, 1216 Crosley Tower: Arup Bose, Indian Statistical Institute, TBA Dept Economics Seminar
  11. Nov 23: seminar cancelled
  12. Nov 30: Wojtek Matysiak Random sequences with linear regressions

Probability Seminar Summer 2005

  • Sergey Utev (June)
  • Janusz Wysoczanski (Wroclaw, Poland) July 11-July 31.
  • Jacek Wesolowski (Warsaw, Poland) August 10-24.

Probability Seminar Spring 2005

  • April 4: Wlodek Bryc Conditional moments, gamma, free gamma, and free Poisson laws Slides
  • April 11: Magda Peligrad: Lp maximal inequality for martingale like sequences
  • April 14, Thursday (Colloquium)Wei Biao Wu Fourier and wavelet transforms of stationary processes
  • April 15, Friday, 3-4PM, Room: 532 Old Chem Wei Biao Wu Kernel Estimation for Time Series
  • April 18: Wlodek Bryc: Slides
  • April 25: Magda Peligrad
  • May 2: Wlodek Bryc (more details for the picture)
  • May 9: seminar cancelled
  • May 16: seminar cancelled
  • May 23: Magda Peligrad, On the weak invariance principle for stationary sequences under projective criteria

Probability Seminar Winter 2005

  • Tue, Jan 18, Noon: Tamer's Advanced Exam
  • Mo, Jan 25: Magda Peligrad: Coupling techniques
  • Mo, Jan 31: Wlodek Bryc: Quadratic harnesses and martingale polynomials
  • Mo, Feb 7: Magda Peligrad: Linear processes with martingale-like innovations
  • Mo, Feb 14: Tamer Oraby, The semicircle law
  • Mo, Feb 21: Wlodek Bryc: Talagrand's concentration of measure
  • Mo, Feb 28: Tamer Oraby, The semicircle law, continued
  • Mo, March 7: Wlodek Bryc, Introduction to Wishart matrices

Probability Seminar Fall 2004

Time: Mondays 2-3.
  • Th, Sept 23, 4PM: Marek Bozejko, Wroclaw Univ., Poland The von Neumann inequality .
  • Oct 4: Magda Peligrad On the characteristic function for sums of dependent random variables
  • Oct 11: Wlodek Bryc Semicircle law, random matrices, and free cumulants This is a combinatorizal slant on the previous analytic Free convolution talk of March 10, 2004. Topics for this talk are: CLT, cumulants, freeness.
  • Oct 18: Wlodek Bryc (cont...) Topics for this talk are: Classical cumulants, free cumulants, freeness. Based on Cumulants in noncommutative probability I by F. Lehner
  • Oct 25: Wlodek Bryc (cont...) Topics for this tsalk are: a regression lemma for free variables (joint with M. Bozejko) and related open questions.
  • Nov 1 (change your clock!!!): Magda Peligrad: Invariance principles for martingale like sequences
  • Nov 8: Magda Peligrad: CLT for linear processes
  • Nov 5: Jeesen Chen On some inequalities
  • Nov 22: Wlodek Bryc, Spectra of large random matrices.
  • Nov 29, 2-4PM, Computer Lab 825: Tamer Oraby, The Limiting Spectral Laws of Block Toeplitz Random Matrices.

Probability Seminar 2004 (Summer)

  • Aug 2, 2PM: Joe Sheehy will present Etemadi's proof of SLLN
    3PM: Tamer Oraby may explain Stein's method, or Wlodek Bryc may talk about random matrices.
  • Aug 6, NOON: Prelim Problem session
  • Aug 9, 2PM: Joe Sheehy will explain how to construct conditional expectations
  • Aug 16, 2PM: Michael Anshelevich, UC Riverside: Combinatorial stochastic measures: an alternative approach to multiple stochastic integrals

Summer visitors

  • August 14-20: Michael Anshelevich, UC Riverside
    Seminar: Aug 16, 2PM Combinatorial stochastic measures: an alternative approach to multiple stochastic integrals
  • August 24 - Sept 15: Jacek Wesolowski, Warsaw Univ. of Techn., Poland
  • August 24 - Sept 8: Wojciech Matysiak Warsaw Univ. of Techn., Poland
  • September 15- October 8: Marek Bozejko, Wroclaw University, Poland
    Colloquium [September 23, 4PM] Kchinchine inequality in classical and non-commutative probability with applications to operator algebras

Probability Seminar 2004 (Spring)

Schedule

  • March 29: Wlodek Bryc: Biane's proof of Borovkov-Utev's Theorem. Based on P. Biane, Logarithmic Sobolev inequalitites, matrix models and free entropy, Acta Math. Sinica. Vol 19, No3, (2003), 1-11
  • April 5: Jeesen Chen, Unsmoothing inequality
  • April 12: Jeesen Chen Unsmoothing inequality (continued)
  • April 19: Magda Peligrad, Maximal inequalities for martingale-like sequences (continued)
  • April 26: none
  • May 3: Wlodek Bryc Spectral measure of large random Hankel , Markov , and Toeplitz matrices
  • May 10: Cancelled
  • May 17: Wlodek Bryc Harnesses, polynomial martingales, free Levy processes
  • May 24: Jeesen Chen Covariance kernell and its applications
  • Colloquium May 27 (Th): Rick Bradley (Indiana University), Pairwise independence, triple-wise independence, and the central limit theorem
  • Special Probab Seminar May 28 (Friday!) 4-5PM in Seminar Room 807: Rick Bradley (Indiana University), On a stationary, triple-wise independent, absolutely regular counterexample to the central limit theorem
    This seminar talk will treat in more detail the topic of the Colloquium talk. It will focus on two particular examples of strictly stationary, triple-wise independent random sequences for which the central limit theorem fails. One of the examples has two states and is ergodic. The other has three states and satisfies a stronger condition known as absolute regularity.
  • May 31: no seminar (Memorial Day)
  • Colloquium June 3 (Th) Florence Merlevède (Univ. Paris VI), Limit Theorems and Deviation Probability of Cramer-von Mises Statistics Drawn from Dependent Random Variables

FA Seminar We 2-3 Room 708

    • April 14: Bogdan Vishnesku Free probability
    • April 21: Bogdan Vishnesku Free probability (cont)
    • April 28: Bogdan Vishnesku Free probability (cont)
    • May 5: Bogdan Vishnesku Free probability (cont)
    • May 12: Bogdan Vishnesku Free probability (cont)
    • May 19: Bogdan Vishnesku Free probability (cont)
    • May 26: Bogdan Vishnesku Free probability (cont)

Probability Seminar 2004 (Winter)

  • Feb 18: Jacek Wesolowski, Matsumoto-Yor property
  • Feb 25: Magda Peligrad, Maximal inequalities for martingale-like sequences
  • March 3: Tamer Oraby: Random walks on Random trees and their fractal dimension.
  • March 10: Wlodek Bryc: Free convolutions of measures
  • March 17: Final Exams - no seminar
  • March 24: Sergey Utev: Operator inequalities and applications to probability, Time: 2-3PM. Place: Seminar Room 807

Probability Seminar 2003 (Autumn)

  • Sept 18, M. Bozejko

Probability Seminar 2002 (Winter)

  • Jan 15, 10-11 (special time for this talk only): W. Bryc, V. Kaftal Covariance Estimates for q-Gaussian processes
  • Jan 22: W. Bryc Random matrices
  • Jan 28: Magda Peligrad Inequalities for moments of partial sums
  • Feb 5: Magda Peligrad Inequalities ... (continued)
  • Feb 12: Wlodek Bryc Random matrices ... (cont.)
  • Feb 19: Jeesen Chen Stein's Methods for CLT
  • Feb 26: Jeesen Chen Stein's Methods for CLT... (cont.)
  • March 5: TBA

Probability Seminar 2001 (Winter)

  • Jan 4: Organizational meeting
  • Jan 11: Jeesen Chen Lovasz Local Lemma(II)
  • Jan 18: Hurlee Gonchigdanzan Almost sure limit theorem for the maximum of the stationary Gaussian sequence
  • Jan 25: Hurlee (cont.)
  • Feb 1: Hurlee (cont.)
  • Feb 8: Magda Peligrad Maximal inequalities
  • Feb 15: Wlodek Bryc q-Gaussian distribution
  • Feb 22: Wlodek Bryc (continued)
  • Mar 1: Daniel Stancescu TBA
  • Mar 8: no seminar

Probability Seminar 2000

  • Oct 5, Organizational meeting. Wlodek Bryc: Non-commutative probability
  • Oct 12, Magda Peligrad: Inequalities for weak dependence
  • Oct 19 - no seminar
  • Oct 26, Ilya Gikhman:Stochastic integrals with applications to physics/finanses
  • Nov 2, Yizong Cheng: Probability Problems in Bioinformatics
  • Nov 9, Yizong Cheng - continued
  • Nov 16, Hurlee Khurelbaartar Gonchigdazan: Almost sure limit theorem for nonlinear functionals of dependent variables
  • Nov 23 - no seminar
  • Nov 30, Daniel Stancescu: Bootstrap