This semester the regular meeting time of our seminar is
Mon 4:45-5:40pm, French Hall 4206.
Please email yizao.wang@uc.edu
if you want to be added to our email list or have any questions.
- Jan 9, Semester starts. Volunteer?
Or shall we skip?
- Jan 16, MLK, no meeting
- Jan 23, Yizao Wang, A new family of random sup-measures
We introduce a new family of stationary and self-similar random sup-measures. The representation of such a random sup-measure is based on intersections of independent stable regenerative sets. This family of random sup-measures arises in limit theorems of extremes of a family of stationary infinitely divisible processes with long range dependence.
The main part of the talk will be devoted to the representation of these random sup-measures.
Joint work with Gennady Samorodnitsky.
- Jan 30, Wlodek Bryc, On the height function for a stationary totally asymmetric exclusion process (TASEP) with open boundary
This is a follow up on Zhipeng's talk at the end of last semester ( TASEP on a ring in relaxation time scale), who presented precise asymptotic for the height function of TASEPs with periodic boundary conditions, started from various initial conditions. I will talk about what is known about height function from physics literature for a stationary TASEP with open boundary. I will also present a plan for a new approach to height function which gives simple answers in special cases, and that should work for the height function of a more general stationary ASEP. Finally, I will point out some natural open questions that are not addressed in physics literature.
- Feb 6, Joseph Najnudel, On random multiplicative functions
In this talk, we give a general presentation of random multiplicative functions on the integers and their main properties. At the end of the talk, we state some results, proven in a preprint recently submitted, on the behaviour and the independence properties of such functions taken at consecutive integers.
- Feb 13, Valentin Bahier. Institut de Mathématiques de Toulouse, On the number of eigenvalues of permutation matrices on intervals of the unit circle
In this talk we will focus on the ensemble of permutation matrices following the uniform distribution. First of all, we will introduce the permutation matrices and give some basic properties about their spectrum. Then, we will describe how the eigenvalues are distributed, considering the counting function of eigenvalues. Finally, we will give a sketch of proof of our results with the help of a convenient tool called "Feller coupling".
- Feb 20, Magda Peligrad. Central limit theorem for discrete double Fourier series of random fields
The talk is motivated by the properties surrounding the spectral density of a process and of a random field. We start by presenting a characterization of the spectral density in function of projection operators on sub-sigma fields. We also point out that the limiting distribution of the real and the imaginary part of the Fourier transform of a stationary random field is almost surely an independent vector with Gaussian marginal distributions, whose variance is, up to a constant, the field’s spectral density. The dependence structure of the random field is general and we do not impose any conditions on the speed of convergence to zero of the covariances, or smoothness of the spectral density. The only condition required is that the variables are adapted to a partially commuting filtration and are regular in some sense. The results go beyond the Bernoulli fields and apply to both short range and long range dependence. The method of proof is based on new probabilistic methods based on martingale approximations and also on borrowed tools from harmonic analysis.
- Feb 27, Na Zhang.
On the normal approximation for random fields via martingale methods
We prove a central limit theorem for strictly stationary random fields under a
sharp projective condition. The assumption was introduced in the setting of
random variables by Maxwell and Woodroofe. Our approach is based on new
results for triangular arrays of martingale differences, which have interest
in themselves.
- Mar 9, Alexey Kuznetsov, York University. The hitchhiker's guide to Levy processes
Department Colloquium, 4-5pm, 240 WCharlton.
What is the connection between the financial time series and grazing patterns of bacteria, cash flows of insurance companies and fluctuations and transport in plasma, seismic series and spreading of epidemic processes? The answer is: Levy processes, which are used in modeling all of these diverse phenomena. I will begin this talk with a gentle introduction to Levy processes followed by some of their applications. Then I will focus on exponential functionals of Levy processes, and I will describe how they fit in the theory of positive self-similar Markov processes in general and stable processes in particular. After discussing some analytical tools and techniques which are used in studying the exponential functional, I will explain why the Answer to the Great Question of Life, the Universe and Stable Processes is exactly forty-two.
- Mar 13, Spring break, no meeting
- Mar 20, Ju-Yi Yen. On Markov processes, their excursions and related sigma-finite measures
In this talk, we relate some finite and sigma-finite measures constructed from Markov processes. Two settings will be discussed: the continuous time diffusions and the recurrent Markov chain.
- Mar 27, Jack Silverstein, NCSU. On the eigenvectors of large dimensional sample covariance matrices
Let $M_n=(1/N)V_nV_n^T$ where $V_n=(v_{ij})$ $i=1,2,\ldots,n$; $j=1,2,\ldots,N=N(n)$, the $v_{ij}$'s are i.i.d. standardized random variables, and $n/N\to c>0$ as $n\to\infty$. $M_n$ can be viewed as a sample covariance matrix formed from the $N$ columns of $V_n$. When $v_{11}$ is standard normal, the orthogonal matrix, $O_n$ of eigenvalues of $M_n$ is Haar distributed in the group of $n\times n$ orthogonal matrices. A review of past attempts to compare $O_n$ with Haar measure when $v_{11}$ is not Gaussian for $n$ large will be given. Recent results will then be presented which extend an earlier result on eigenvector behavior.
- April 1-2, AMS Meeting at Bloomington
- Apr 10, Yi Shen, University of Waterloo. Probabilistic symmetries and random locations
In this talk we briefly discuss different types of symmetries in probability, including stationarity, stationarity of the increments, isotropy, self-similarity and their combinations. Each of these symmetries can be expressed as the invariance of the distribution of the stochastic processes with respect to certain action. In particular, we consider the random locations of stochastic processes, such as the hitting times or the location of the path supremum over a fixed interval. On one hand, we see how the probabilistic symmetries can imply the properties of the distributions of these random locations; on the other hand, we also discuss how the distributions of the random locations can be used to characterize the probabilistic symmetries. We then proceed to propose a unified framework to study the random locations for stochastic processes exhibiting probabilistic symmetries.
- Apr 20, Davar Khoshnevisan, University of Utah. Canceled
I will describe ongoing efforts, with Kunwoo Kim and Yimin Xiao, toward a large-scale multifractal description of the tall peaks of the solution to a family of randomly-forced partial differential equations that are known to undergo “intermittency,” and arise in several areas of mathematics and its applications.
- Apr 24, Exam Week.
Past Seminar Archives (with photos!!)
Past Probability Events at UC
Other Probability Conferences
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