Random matrices and random partitions at varying temperatures

I will discuss the global-scale behavior of ensembles of random matrix eigenvalues and random partitions which depend on the “inverse temperature” parameter beta. The goal is to convince the audience of the effectiveness of the moment method via Fourier-like transforms in characterizing the Law of Large Numbers and Central Limit Theorems in various settings. We focus on the regimes of high and low temperatures, that is, when the parameter beta converges to zero and infinity, respectively. Part of this talk is based on joint projects with F. Benaych-Georges — V. Gorin, and M. Dolega — A. Moll.