Bulk universality for one-dimensional log-gases

Research output: Chapter in Book/Report/Conference proceedingChapter

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 languageEnglish (US)
Title of host publicationXVIIth International Congress on Mathematical Physics
Subtitle of host publicationAalborg, Denmark, 6-11 August 2012
PublisherWorld Scientific Publishing Co.
Pages404-416
Number of pages13
ISBN (Electronic)9789814449243
ISBN (Print)9789814449236
DOIs
StatePublished - Jan 1 2013

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Keywords

  • Log-gas
  • Universality
  • β-ensembles

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Bourgade, P. (2013). Bulk universality for one-dimensional log-gases. In XVIIth International Congress on Mathematical Physics: Aalborg, Denmark, 6-11 August 2012 (pp. 404-416). World Scientific Publishing Co.. https://doi.org/10.1142/9789814449243_0034