Nicholas Cook (Duke University)

Title: The maximum of Poissonian log-correlated fields

Abstract: Extreme values of logarithmically correlated fields have been extensively studied in connection with branching processes, reaction-diffusion PDE, random matrices, Gaussian multiplicative chaos, and L-functions in number theory. The sharpest results are for Gaussian or nearly-Gaussian fields; however, some objects in random matrix theory and number theory 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'll discuss a refined result for a related class of random trigonometric polynomials, for which 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).