Universality for a class of random band matrices

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

Research output: Contribution to journalArticle

Abstract

We prove the universality for the eigenvalue gap statistics in the bulk of the spectrum for band matrices, in the regime where the band width is comparable with the dimension of the matrix, W ~ N. All previous results concerning universality of non-Gaussian random matrices are for mean-field models. By relying on a new mean-field reduction technique, we deduce universality from quantum unique ergodicity for band matrices.

Original languageEnglish (US)
Pages (from-to)739-800
Number of pages62
JournalAdvances in Theoretical and Mathematical Physics
Volume21
Issue number3
DOIs
StatePublished - 2017

Fingerprint

Band matrix
Random Matrices
Universality
matrices
Mean-field Model
Ergodicity
Mean Field
Deduce
eigenvalues
Bandwidth
statistics
Statistics
Eigenvalue
bandwidth
Class

Keywords

  • Band matrices
  • Dyson Brownian motion
  • Quantum unique ergodicity
  • Universality

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)

Cite this

Universality for a class of random band matrices. / Bourgade, Paul; Erdoos, Laszlo; Yau, Horng Tzer; Yin, Jun.

In: Advances in Theoretical and Mathematical Physics, Vol. 21, No. 3, 2017, p. 739-800.

Research output: Contribution to journalArticle

Bourgade, Paul ; Erdoos, Laszlo ; Yau, Horng Tzer ; Yin, Jun. / Universality for a class of random band matrices. In: Advances in Theoretical and Mathematical Physics. 2017 ; Vol. 21, No. 3. pp. 739-800.
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