Charlie Dworaczek Guera: The β-ensembles at high temperature

Abstract:

In this talk, we will explore the high-temperature regime of the well-known β-ensembles. In this regime, the inverse temperature β scales as 1/N, where N is the number of particles. A key characteristic of this regime is that entropic effects become significant, in contrast to the classical regime. This results in the fact that the limit of the empirical measure is supported on the whole real line. I will review the existing literature, present the CLT, the all-order asymptotic expansion of the partition function and a large deviation principle for the largest particle. It includes joint works with Ronan Memin (IMToulouse).