A local CLT for linear statistics of 2D Coulomb gases
arXiv:2005.12163
Abstract
We prove a local central limit theorem for fluctuations of linear statistics of smooth enough test functions under the canonical Gibbs measure of two-dimensional Coulomb gases at any positive temperature. The proof relies on the existing global central limit theorem and a new decay estimate for the characteristic function of such fluctuations.
15p Final version, to appear in Markov Processes and Related Fields