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2018 CLT for Fluctuations of $\beta $-ensembles with general potential
Florent Bekerman, Thomas Leblé, Sylvia Serfaty
Electron. J. Probab. 23: 1-31 (2018). DOI: 10.1214/18-EJP209

Abstract

We prove a central limit theorem for the linear statistics of one-dimensional log-gases, or $\beta $-ensembles. We use a method based on a change of variables which allows to treat fairly general situations, including multi-cut and, for the first time, critical cases, and generalizes the previously known results of Johansson, Borot-Guionnet and Shcherbina. In the one-cut regular case, our approach also allows to retrieve a rate of convergence as well as previously known expansions of the free energy to arbitrary order.

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Florent Bekerman. Thomas Leblé. Sylvia Serfaty. "CLT for Fluctuations of $\beta $-ensembles with general potential." Electron. J. Probab. 23 1 - 31, 2018. https://doi.org/10.1214/18-EJP209

Information

Received: 6 February 2018; Accepted: 4 August 2018; Published: 2018
First available in Project Euclid: 24 November 2018

zbMATH: 07021671
MathSciNet: MR3885548
Digital Object Identifier: 10.1214/18-EJP209

Subjects:
Primary: 60B10, 60B20, 60F05, 60G15, 60K35, 82B05

JOURNAL ARTICLE
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Vol.23 • 2018
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