Nicholas Cook
Duke University
Title
The maximum of Poissonian log-correlated fields
Abstract
Extreme values of logarithmically correlated fields have been extensively studied due to connections with Gaussian multiplicative chaos, random matrices, branching random walks, reaction-diffusion PDE, and L-functions in analytic number theory. The sharpest results are for Gaussian or nearly-Gaussian fields. On the other hand, characteristic polynomials of sparse random matrices give rise to log-correlated fields with Poissonian tails. In prior work with Zeitouni we obtained the leading order of the maximum for the characteristic polynomial of random permutation matrices. I will discuss a refined result on the maximum for a related class of random trigonometric polynomials. We find the behavior of extremes is modeled by a branching random walk in random time-environment. Based on joint work with Haotian Gu (UCLA).