Probability Seminar

Date Time 
Location  Speaker 
Title – click for abstract 

09/18 3:15pm 
BLOC 220 
Boris Hanin TAMU 
Local Universality for Random Waves on Riemannian Manifolds
Random waves on a Riemannian manifold are a Gaussian model for eigenfunctions of the Laplacian. This model first arose in Berry's random wave conjecture from the 1970's, which states that random waves are good semiclassical models for deterministic wavefunctions in chaotic quantum systems. I will explain what this means and give some examples of why this conjecture is so far from being proved. I will then talk about some ongoing work with Yaiza Canzani about local universality for random waves. The idea is that, just like for random matrix models, random waves have universal scaling limits under some generic assumptions. This local universality allows one to say quite a bit about the size and topology (e.g. number of connected components) of zero sets of random waves. I will state some of these results and a few open questions as well. 

09/25 3:00pm 
BLOC 220 
Gilles Pisier TAMU & Paris 6 
Subgaussian random variables and generalizations


10/09 10:00am 
BLOC 220 
Eviatar Procaccia and Yuan Zhang TAMU 
On covering monotonic paths with simple random walk
We study the probability that a $d$ dimensional simple random walk (or the first $L$ steps of it) covers each point in a nearest neighbor path connecting 0 and the boundary of an $L_1$ ball. We show that among all such paths, the one that maximizes the covering probability is the monotonic increasing one that stays within distance 1 from the diagonal. As a result, we can obtain an exponential upper bound on the decaying rate of covering probability of any such path when d≥4 and a $\log$ correction for $d=3$. Interesting conjectures and open questions will be presented.
The talk will be split between Eviatar and Yuan. Eviatar will present the background and Yuan the combinatorics part. 

11/03 10:00am 
BLOC 220 

UT Austin  TAMU probability day
https://sites.google.com/site/austintamuprob/
Please register by October 25th. 

11/20 3:00pm 
BLOC 220 
Jiayan Ye TAMU 
Continuity of cheeger constant in supercritical percolation
Abstract: We consider the supercritical bond percolation on $Z^d$ with $d \geq 3$ and $p > p_c(Z^d)$. In particular, we study the subgraphs of $C_{\infty} \cap [n, n]^d$ with minimal cheeger constant, where $C_{\infty}$ is the unique infinite open cluster on $Z^d$. Recently, Gold proved that the subgraphs converge to a deterministic shape almost surely. We prove that this deterministic shape is Hausdrorff  continuous in the percolation parameter $p$. This is joint work with Eviatar Procaccia.

Archives
Please direct inquiries to
Eviatar Procaccia.