Bulk universality for one-dimensional log-gases

P. Bourgade

doi:10.1142/9789814449243_0034

Bulk universality for one-dimensional log-gases

P. Bourgade

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

In this note we consider β-ensembles with real analytic potential and arbitrary inverse temperature β, and review some recent universality results for these measures, obtained in joint works with L. Erdős and H.-T. Yau. In the limit of a large number of particles, the local eigenvalues statistics in the bulk are universal: they coincide with the spacing statistics for the Gaussian β-ensembles. We also discuss the proof of the rigidity of the particles up to the optimal scale N^−1+ε.

Original language	English (US)
Title of host publication	XVIIth International Congress on Mathematical Physics
Subtitle of host publication	Aalborg, Denmark, 6-11 August 2012
Publisher	World Scientific Publishing Co.
Pages	404-416
Number of pages	13
ISBN (Electronic)	9789814449243
ISBN (Print)	9789814449236
DOIs	https://doi.org/10.1142/9789814449243_0034
State	Published - Jan 1 2013

Keywords

Log-gas
Universality
β-ensembles

ASJC Scopus subject areas

General Physics and Astronomy

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10.1142/9789814449243_0034

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AB - In this note we consider β-ensembles with real analytic potential and arbitrary inverse temperature β, and review some recent universality results for these measures, obtained in joint works with L. Erdős and H.-T. Yau. In the limit of a large number of particles, the local eigenvalues statistics in the bulk are universal: they coincide with the spacing statistics for the Gaussian β-ensembles. We also discuss the proof of the rigidity of the particles up to the optimal scale N−1+ε.

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KW - Universality

KW - β-ensembles

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BT - XVIIth International Congress on Mathematical Physics

PB - World Scientific Publishing Co.

ER -

Bulk universality for one-dimensional log-gases

Abstract

Keywords

ASJC Scopus subject areas

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