The Eigenvector Moment Flow and Local Quantum Unique Ergodicity

Paul Bourgade, H. T. Yau

Research output: Contribution to journalArticle

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)1-48
Number of pages48
JournalCommunications in Mathematical Physics
DOIs
StateAccepted/In press - Apr 30 2016

Fingerprint

Ergodicity
Eigenvector
eigenvectors
Moment
moments
Finite Speed of Propagation
maximum principle
normality
Random Environment
Maximum Principle
Asymptotic Normality
random walk
entry
regularity
Brownian motion
Random walk
Regularity
propagation
estimates
matrices

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

The Eigenvector Moment Flow and Local Quantum Unique Ergodicity. / Bourgade, Paul; Yau, H. T.

In: Communications in Mathematical Physics, 30.04.2016, p. 1-48.

Research output: Contribution to journalArticle

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