Extrema of the Characteristic Polynomial of CβE Matrices

Explore the mathematical properties of logarithmically correlated fields through this 58-minute lecture examining the extrema of characteristic polynomials of CβE matrices. Delve into groundbreaking research that validates the famous Fyodorov–Hiary–Keating conjecture by analyzing how the logarithm of the characteristic polynomial, when viewed as a function on the unit circle in the complex plane, behaves as a logarithmically correlated field. Learn about joint work with Elliot Paquette that proves the properly centered maximum of this field converges to the sum of a Gumbel random variable and an independent random variable Z. Discover recent advances in identifying the specific properties of the random variable Z and understand the mathematical techniques used to establish these convergence results. Gain insights into the intersection of random matrix theory, probability theory, and complex analysis through this advanced mathematical presentation delivered by Ofer Zeitouni at the Simons Foundation.