Speaker
Byun, Seoul National University
Abstract
Characteristic polynomials play a central role in random matrix
theory, with deep connections to statistical mechanics, Coulomb gases, and
integrable systems. In this talk, I will discuss several recent results on
moments of characteristic polynomials for non-Hermitian random matrix
ensembles and their relation to free energy asymptotics. I will describe how
characteristic polynomial moments can be used to investigate free energy
expansions in a variety of non-Hermitian models and Coulomb gas systems.
These results reveal a number of common asymptotic structures and suggest new
perspectives on statistical mechanical quantities associated with random
matrices. I will also discuss a duality principle that relates certain
non-Hermitian random matrix models to observables arising in integrable
probability. As an illustration, I will explain a recent connection to last
passage percolation and some of its asymptotic consequences.