Fixed Energy Universality for Generalized Wigner Matrices

Paul Bourgade, Laszlo Erdős, Horng Tzer Yau, Jun Yin

Research output: Contribution to journalArticlepeer-review


We prove the Wigner-Dyson-Mehta conjecture at fixed energy in the bulk of the spectrum for generalized symmetric and Hermitian Wigner matrices. Previous results concerning the universality of random matrices either require an averaging in the energy parameter or they hold only for Hermitian matrices if the energy parameter is fixed. We develop a homogenization theory of the Dyson Brownian motion and show that microscopic universality follows from mesoscopic statistics.

Original languageEnglish (US)
Pages (from-to)1815-1881
Number of pages67
JournalCommunications on Pure and Applied Mathematics
Issue number10
StatePublished - Oct 1 2016

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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