A local CLT for linear statistics of 2D Coulomb gases
Abstract
We prove a local central limit theorem for fluctuations of linear statistics of smooth enough test functions under the canonical Gibbs measure of twodimensional 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.
 Publication:

arXiv eprints
 Pub Date:
 May 2020
 arXiv:
 arXiv:2005.12163
 Bibcode:
 2020arXiv200512163L
 Keywords:

 Mathematics  Probability;
 Mathematical Physics
 EPrint:
 15p Final version, to appear in Markov Processes and Related Fields