Probability Seminar

Date Time 
Location  Speaker 
Title – click for abstract 

09/06 11:30am 
BLOC 628 
Boris Hanin TAMU 
Products of Many Large Random Matrices
I will present some recent joint work with Mihai Nica (Toronto) and ongoing work with Grigoris Paouris (Texas A&M) about products of N independent matrices of size n x n in the regime where both the size n and the number of terms N tends to infinity. I will discuss in particular the work in progress with Paouris that gives finite size corrections to the multiplicative ergodic theorem regime in which the N is much larger than n. 

09/20 11:30am 
BLOC 628 
Jiayan Ye (Prelim exam) TAMU 
On Stationary DLA.
Diffusion limited aggregation (DLA) in $\mathbb{Z}^2$ is a
stochastic process first defined by Witten and Sander in order to study
aggregation systems governed by diffusive laws. In this talk, I will
construct an infinite stationary DLA on the upper half planar lattice.
The stationary DLA is ergodic with respect to integer leftright
translations. This is a joint work with Eviatar Procaccia and Yuan
Zhang. 

09/27 11:30am 
BLOC 628 
Patricia Alonso Ruiz TAMU 
Order statistics in stochastic geometry
This talk will discuss and give an overview of questions concerning the asymptotic distribution of order statistics for functionals of spatial Poisson point processes. We will highlight some techniques from stochastic geometry applied in this setting. 

10/04 11:30am 
BLOC 628 
Axel Sáenz Tulane 
Stationary dynamics in finite time for the totally asymmetric simple exclusion process
The totally asymmetric simple exclusion process (TASEP) is a
Markov process that is the prototypical model for transport phenomena in
nonequilibrium statistical mechanics. It was first introduced by
Spitzer in 1970, and in the last 20 years, it has gained a strong
resurgence in the emerging field of "Integrable Probability" due to
asymptotic results from Johansson in 2000 and Tracy and Widom in 2007
(among other related results). In particular, these formulas led to
great insights regarding fluctuations related to the TracyWidom
distribution and scalings to the KardarParisiZhang (KPZ) stochastic
differential equation.
In this joint work with Leonid Petrov (University of Virginia), we
introduce a new and simple Markov process that maps the distribution of
the TASEP at time t>0 , given step initial time data, to the
distribution of the TASEP at some earlier time t−s>0. This process "back
in time" is closely related to the Hammersley process introduced by
Hammersley in 1972, which later found a resurgence in the longest
increasing subsequence problem in the work of Aldous and Diaconis in
1995. Hence, we call our process the backwards Hammersleytype process
(BHP). As a fun application of our results, we have a new proof of the
limit shape for the TASEP. The central objects in our constructions and
proofs are the Schur point processes and the YangBaxter equation for
the sl_2 quantum affine Lie algebra. In this talk, we will discuss the
background in more detail and will explain the main ideas behind the
constructions and proof. 

10/18 11:30am 
BLOC 628 
LouisPierre Arguin CUNY 
Large Values of the Riemann Zeta Function in Short Intervals
In a seminal paper in 2012, Fyodorov & Keating proposed a series of conjectures describing the statistics of large values of zeta in short intervals of the critical line. In particular, they relate these statistics to the ones of logcorrelated Gaussian fields. In this lecture, I will present recent results that answer many aspects of these conjectures. Connections to problems in number theory will also be discussed. 

10/25 11:30am 
BLOC 628 
Hanbaek Lyu UCLA 
TBA
TBA 

11/01 11:30am 
BLOC 628 
Quan Zhou TAMU (Statistics) 
Optimal detection of a drifting Brownian coordinate
Given a stochastic process X_t, how to find a stopping time \tau that maximizes the expectation of some reward function, say G(X_\tau), is known as an optimal stopping problem. Two famous examples are the secretary problem and the pricing of American options. Interestingly, continuoustime optimal stopping problems can often be converted to freeboundary PDE problems. The primary goal of this talk is to introduce the theory of optimal stopping using a class of problems which we refer to as “optimal detection of a drifting Brownian coordinate”: Imagine N independent Brownian motions. One of them has a nonzero drift while all the others are just standard Brownian motions. The question is how to find out which one is drifting as soon as possible. This problem can be formulated in many ways. In this talk we will focus on one particular formulation as an optimal stopping problem and solve the corresponding free boundary problem. Some other formulations will be briefly discussed as well. We will also mention applications of the optimal stopping theory (and more generally stochastic optimization) in statistics. 
Please direct inquiries to
Eviatar Procaccia.