Combinatorics Seminar - Elliot Paquette

September 18, 2018
Thursday, September 20, 2018 - 10:20am to 11:15am
Cockins Hall 240
Combinatorics Seminar

Title: Random matrix point processes via stochastic processes

Speaker: Elliot Paquette (The Ohio State University)

Abstract: In 2007, Virág and Válko introduced the Brownian carousel, a dynamical system that describes the eigenvalues of a canonical class of random matrices. This dynamical system can be reduced to a diffusion, the stochastic sine equation, a beautiful probabilistic object requiring no random matrix theory to understand. This talk will show how this dynamical system arises and describe the stochastic sine equation in a non--technical way.

Many features of the eigenvalues of the random matrix can then be studied via this stochastic process. We will sketch how this stochastic process is connected to eigenvalues of a random matrix and how problems relating to the eigenvalues of this process can be tackled using this stochastic process.

Based on joint works with Diane Holcomb, Gaultier Lambert, Bálint Vet\H{o}, and Bálint Virág.

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