The Eigenvector Moment Flow and Local Quantum Unique Ergodicity

P. Bourgade, H. T. Yau

Research output: Contribution to journalArticle


We prove that the distribution of eigenvectors of generalized Wigner matrices is universal both in the bulk and at the edge. This includes a probabilistic version of local quantum unique ergodicity and asymptotic normality of the eigenvector entries. The proof relies on analyzing the eigenvector flow under the Dyson Brownian motion. The key new ideas are: (1) the introduction of the eigenvector moment flow, a multi-particle random walk in a random environment, (2) an effective estimate on the regularity of this flow based on maximum principle and (3) optimal finite speed of propagation holds for the eigenvector moment flow with very high probability.

Original languageEnglish (US)
Pages (from-to)231-278
Number of pages48
JournalCommunications In Mathematical Physics
Issue number1
StatePublished - Feb 1 2017


ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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