A local CLT for linear statistics of 2D Coulomb gases
Probability
2021-06-24 v3 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.2005.12163,
title = {A local CLT for linear statistics of 2D Coulomb gases},
author = {Thomas Leblé and Ofer Zeitouni},
journal= {arXiv preprint arXiv:2005.12163},
year = {2021}
}
Comments
15p Final version, to appear in Markov Processes and Related Fields