Bulk universality for one-dimensional log-gases

Research output: Chapter in Book/Report/Conference proceedingChapter


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.
Number of pages13
ISBN (Electronic)9789814449243
ISBN (Print)9789814449236
StatePublished - Jan 1 2013


  • Log-gas
  • Universality
  • β-ensembles

ASJC Scopus subject areas

  • General Physics and Astronomy


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