Ofer Zeitouni
Title
Random matrices and logarithmically correlated fields.
Abstract
Random matrices have been introduced in statistics as models of data, and in physics as models for the Hamiltonian of heavy nuclei. They found applications in many branches of mathematics, including probability theory, number theory, and mathematical physics. I will introduce the basic models and focus on the study of the characteristic polynomial as a (random) field indexed by subsets of the complex plane. Focusing on the so called C$\beta$E model, I will explain the Fyodorov-Hiary-Keating conjecture (random matrix side) and its resolution. If time permits, I will discuss links with the Riemann zeta function.
