Probability and Mathematical Physics Seminar

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Probability and the City seminar

Speaker: Simona Diaconu (Courant) and Yu Gu (University of Maryland)

Location: Columbia University, Mathematics Hall, 2990 Broadway 203

Date: Friday, September 29, 2023, 10 a.m.

Synopsis:

The Probability and the City seminar is a joint meeting of the probability seminars at Courant and at Columbia, held twice every semester (hosted once at each institution).
The first meeting of Fall 2023 will feature:

• Simona Diaconu (Courant)
  Title: Traces, Eigenvalues, and Eigenvectors Abstract

• Abstract: 
  Random matrix theory is concerned primarily with the eigenvalues and eigenvectors of certain ensembles. The method of moments is a common technique in this area: it goes back to Wigner in 1955, and consists of finding the asymptotic behavior of traces of large powers of matrices. The most common uses are operator norm bounds with high probability, a classical result of Soshnikov from 1998 being edge eigenspectrum universality. The purpose of this talk is highlighting the versatility of this technique by presenting three (more) recent applications, two yielding central limit theorems for eigenvalues, and one perhaps even surprising, related to eigenvectors. No background in random matrix theory is assumed.

• Yu Gu (University of Maryland)
  Title: Effective diffusivities in periodic KPZ Abstract
  
  Abstract: 
  It’s known that the KPZ equation on a torus exhibits diffusive behaviors in large time. In this talk, I will discuss the recent joint work with Tomasz Komorowski and Alex Dunlap in which we derived nearly explicit expressions of the diffusion constants. The argument is based on a combination of Malliavin calculus and stochastic homogenization.