A Local CLT for Linear Statistics of 2D Coulomb Gases

T. Leble, O. Zeitouni

2021, v.27, Issue 4, 607-630


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 \textit{global} central limit theorem of \cite{BBNY, LebSerCLT} and a new decay estimate for the characteristic function of such fluctuations.

Keywords: Local central limit theorem, Coulomb gas, loop equations


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