## Probability Seminar Fall 2013

Time and place: Thursdays 1:30 - 2:50 Seminar Room( 4206 French Hall West) Since Fall of 2013, the current seminar page is at https://sites.google.com/site/cincinnatiprobability/home
1. Organizational meeting
2. Sept 5 : Yizao Wang, Order statistics of heavy tailed random variables and applications to random matrices.
3. October 5-6: AMS Fall Southeastern Sectional Meeting University of Louisville, Louisville, KY Special Session on Weak Convergence in Probability and Statistics

## Probability Seminar Spring 2013

Time and place: Fridays 03:35pm 04:30pm Rm 316 Braunstein Hall Rm 608 Swift Hall
1. Fri, Jan 18: Florence Merlevede, Universite Paris 6 Limiting spectral distribution for sample covariance matrices.
2. Thursday, January 24, 2013 from 4:30 . 6:30 PM. 60 West Charlton Building, Room 140 - Martial dissertation defense.
3. Fri, Jan 25: Yizao Wang Limit theorems for linear processes with dependent innovations: a review of two different approaches
4. Fri, Feb 1: Frank Pinski (Physics, UC) Sampling in Path Space - A Physical Application
We are investigating collections of atoms as their positions evolve under Brownian (over-damped Langevin) dynamics. In the cases where the collection changes conformation, an energy barrier often exists. Such transitions are rare events when the thermal energy is small compared to the energy barrier. The understanding of such rare events is the goal of our studies. Consider the position of an atom as a function of time. The time-ordered set of these positions is then a path and is an infinite-dimensional object. Such Brownian paths are continuous but almost nowhere differentiable. I will describe how we derive the measure governing such paths and describe the Hybrid Monte Carlo method we use to sample transition paths. Finally I will display some results for transitions in small atomic clusters.
A. Beskos, F.J. Pinski, J.-M. Sanz-Serna and A.M.Stuart, Hybrid Monte-Carlo on Hilbert Spaces, Stoch. Proc. Applic. 121, 2201-2230 (2011).
5. Feb 8: Wlodek Bryc, Separation of the largest eigenvalues in eigenanalysis of genotype data from discrete subpopulations(based on joint paper with Kasia Bryc and Jack Silverstein)
6. Feb 15: (Advanced Exam) David Barrera will talk about Central Limit Theorem for deterministic systems.
7. Feb 22: Magda
8. March 1 : Cristina Tone (Louisville) Cristina Tone (University of Louisville) Two limit theorems for Strictly Stationary Random Fields Satisfying an Interlaced Mixing Condition
9. March 8: Dalibor Volny On limit theorems for mixing processes
10. Sunday, March 10, 9:20 (Daylight savings time), Campus Rec. Center, Room 3230: Rodrigo Banuelos (Purdue University) Fourier multipliers arising from Lévy processes (This talk is part of The Third Ohio River Analysis Meeting
11. March 15: Stats-Probab Prelim meeting
12. March 22: no seminar (spring break)
13. March 29: Arup Bose (Indian Statistical Institute Kolkata Extreme eigenvalues of random matrices
Abstract: There is a substantial body of literature on the properties of extreme eigenvalues of large dimensional random matrices such as the Wigner matrix, sample covariance matrix, circulant matrix and the Toeplitz matrix. Compared to the behaviour of extreme values of iid observations, the almost sure behaviour and limit laws for extreme eigenvalues are much more complicated to derive and often the limits are not known in any explicit form. We review some of the existing literature in this area and discuss some open issues.
14. Statistics Seminar, Friday April 5, 3:35 pm-4:30 pm Room 130 West Charlton: Dr. Karthik Bharath will be presenting "On a Clustering Criterion for Smooth Distributions"
15. Apr 12: Gerard Letac (Toulouse, Fr) The Dirichlet curve of a probability in $R^d$.
Abstract: If $\alpha$ is a probability in $R^d$ and if $t>0$ the Dirichlet random probability $P$ on $R^d$ governed by $t\alpha$ is such that $(P(A_1),\ldots,P(A_n))$ is Dirichlet distributed with parameters $t(\alpha(A_1),\ldots,\alpha(A_n)$ for any partition $(A_1,\ldots,A_n)$ of $R^d.$ If $\int_{R^d} \log(1+|x|)\alpha(dx)<\infty$ then the random variable $X=\int_{R^d}xP(dx)$ exists. Writing $X\sim\mu(t\alpha)$ the talk will explore the Dirichlet curve of $\alpha,$ namely $t\mapsto \mu(t\alpha).$ We will consider the fixed points, the conjectures about the increasing concentration of $t\mapsto \mu(t\alpha)$ and the asymptotic behavior.
16. Apr 19: ? TBA

Course number: 15 MATH 9059 001

## Probability seminar fall semester 2012

Time and place: We 11:15-12:10 Seminar Room.
1. Taft Lecture Th, Aug 30, 4PM Recreation Center, Room 3210: Persi Diaconis (Stanford) On Coincidences
ABSTRACT: Coincidences astound us. They can affect who we live with and what we work at. I will review work of Jung and Freud. Sometimes, a bit of quantitative thinking can s how that things are not so surprising after all.
2. Colloquium Fri, Aug 31, 4PM Room 819 Swift: Persi Diaconis (Stanford) On adding a List of Numbers (and Other Determinental Point Process)
3. Sept 5: organizational meeting
4. Sept 12: Magda Peligrad Limit theorems for Fourier Transform
5. Sept 19: Jacek Wesolowski (Warsaw) Renorming divergent perpetuities (joint work with Pawel Hitczenko)
6. Sept 26: Arup Bose (Kolkata) Nonrandom and random Toeplitz matrices.
7. Oct 3: Robert Buckingham "Shock clustering and Burger's turbulence"
8. Oct 10: Jeesen Chen "Entropy and the Central Limit Theorem"
9. Oct 17: Yizao Wang "Two problems about extremes, from random walks to statistical mechanics. "
10. Oct 24: Ando (Urns)
11. Oct 31: Ju-yi Yen Skorokhod embeddings and convex order
12. Nov 7: Martial Longla Rho-mixing coefficient for some copula based Markov chains.
I will show the proofs of two theorems on rho-mixing coefficient. The first will be for archimedian copulas with non-strict generator and the second will be for any copula with property $c(x,y)>f(x)+g(y)$.
13. Nov 14: Yizao Wang Limiting distribution for the maximal standardized increment of a random walk (joint work with Zakhar Kabluchko)
14. Nov 21: Wlodek Bryc Generators of Markov processes based on joint work in progress with Jacek Wesolowski.
15. Nov 28: Ando (Urns)
16. Dec 5: Martial Longla TBA

Past Seminars: | Current Year | 2011-12 | 2000-10