Maximum of Poissonian Log-correlated Fields

Explore the extreme value behavior of logarithmically correlated fields with Poissonian tails in this 51-minute seminar lecture. Delve into the mathematical connections between these fields and Gaussian multiplicative chaos, random matrices, branching random walks, reaction-diffusion PDEs, and L-functions in analytic number theory. Learn about the differences between Gaussian and Poissonian logarithmically correlated fields, examining how characteristic polynomials of sparse random matrices generate fields with Poissonian tail behavior. Discover refined results on maximum values for random function series with Poissonian tails, including the sub-leading order behavior that differs significantly from the standard "Bramson correction" term found in Gaussian cases. Understand how this behavior can be modeled using branching random walks in random time-inhomogeneous environments, building upon earlier work by Cook and Zeitouni on permutation matrices and extending to new theoretical developments in probability theory and mathematical physics.