Haotian Gu, UCLA

Title: Maximum of Poissonian Log-correlated Fields

Abstract: Extreme values of logarithmically correlated fields (LCFs) have received lots of interests due to connections with Gaussian multiplicative chaos, random matrices, branching random walks, reaction-diffusion PDEs, 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 LCFs with Poissonian tails. In an earlier work on permutation matrices, Cook and Zeitouni obtained the leading order of the maximum. I will discuss new refined results on the maximum for a related class of random function series with Poissonian tails. We find the sub-leading order behavior is significantly different from the ubiquitous “Bramson correction” term for Gaussian LCFs, and can be modeled by a branching random walk in a random time-inhomogeneous environment. Based on upcoming joint work with Nicholas Cook (Duke).