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arXiv · 2005.12163

A local CLT for linear statistics of 2D Coulomb gases

Thomas Leblé·Ofer Zeitouni
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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.

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Thomas Leblé, Ofer Zeitouni. 2020-05-25. A local CLT for linear statistics of 2D Coulomb gases. https://arxiv.org/abs/2005.12163

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