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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