A Local CLT for Linear Statistics of 2D Coulomb Gases

Thomas Leblé; Ofer Zeitouni

A Local CLT for Linear Statistics of 2D Coulomb Gases

Thomas Leblé
, Ofer Zeitouni

Research output: Contribution to journal › Article › peer-review

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 global central limit theorem of [4, 12] and a new decay estimate for the characteristic function of such fluctuations.

Original language	English
Pages (from-to)	607-630
Number of pages	24
Journal	Markov Processes and Related Fields
Volume	27
Issue number	4
Publication status	Published - 1 Jan 2021
Externally published	Yes

Keywords

Coulomb gas
Local central limit theorem
loop equations

Cite this

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title = "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 two-dimensional Coulomb gases at any positive temperature. The proof relies on the global central limit theorem of [4, 12] and a new decay estimate for the characteristic function of such fluctuations.",

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AU - Zeitouni, Ofer

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Y1 - 2021/1/1

N2 - 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 global central limit theorem of [4, 12] and a new decay estimate for the characteristic function of such fluctuations.

AB - 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 global central limit theorem of [4, 12] and a new decay estimate for the characteristic function of such fluctuations.

KW - Coulomb gas

KW - Local central limit theorem

KW - loop equations

UR - https://www.scopus.com/pages/publications/85147310420

M3 - Article

AN - SCOPUS:85147310420

SN - 1024-2953

VL - 27

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JO - Markov Processes and Related Fields

JF - Markov Processes and Related Fields

IS - 4

ER -

A Local CLT for Linear Statistics of 2D Coulomb Gases

Abstract

Keywords

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