The Eigenvector Moment Flow and Local Quantum Unique Ergodicity

P. Bourgade, H. T. Yau

Research output: Contribution to journalArticlepeer-review

Abstract

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
Volume350
Issue number1
DOIs
StatePublished - Feb 1 2017

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Fingerprint Dive into the research topics of 'The Eigenvector Moment Flow and Local Quantum Unique Ergodicity'. Together they form a unique fingerprint.

Cite this