VIRTUAL SEMINAR SERIES -- INTEGRABLE SYSTEMS: Painlevé transcendents in non-Hermitian random matrix ensembles

Alfredo Deano (University of Kent)

Wednesday 10th June, 2020 14:00-15:00 Zoom seminar hosted by ICMS

Abstract

The connection between NxN Hermitian random matrix ensembles (such as the Gaussian Unitary Ensemble, GUE) and solutions of Painlevé differential equations gives a description of many quantities of interest in random matrix theory, such as distribution of the largest eigenvalue or gap probabilities, in terms of nonlinear special functions. This remarkable connection can be established both for finite N and as N tends to infinity, involving different families of solutions of Painlevé equations. In this talk we will present analogous results obtained recently in the context of non-Hermitian random matrix ensembles, including complex Ginibre and truncated unitary ensembles. 

Joint work with Nick Simm (University of Sussex), based on https://arxiv.org/abs/1909.06334

 

For more information, and how to access the seminar through Zoom, see the webpage of the events here.

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