Time：14:00-16:00, Wednesday, June 10 2026
Venue：E14-116
Speaker：Cesar Cuenca, Ohio State University
Title：Discrete N-particle ensembles at high temperature through symmetric functions
Abstract: Following a brief discussion of the continuous Gaussian beta ensemble and the classical Law of Large Numbers (LLN) for its empirical measures in the regime of fixed temperature, we switch to the setting of discrete-space particle systems. By using Fourier transforms based on Jack symmetric polynomials, we study discrete N-particle ensembles in the regime where the inverse temperature parameter tends to zero, simultaneously as the number of particles in the system tends to infinity. We prove the LLN and characterize the limiting measure in terms of a moment problem. For fixed-time distributions of the discrete beta-Dyson Brownian motion, we calculate the densities of the limiting measures and express them in terms of the zeroes of certain entire functions or the eigenvalues of certain Jacobi operators. This talk is based on joint works with Florent Benaych-Georges, Vadim Gorin and Maciej Dolega.
