Quantum ergodicity on large regular graphs

Nalini Anantharaman, Etienne Le Masson

Research output: Contribution to journalArticle (Academic Journal)peer-review

29 Citations (Scopus)
34 Downloads (Pure)

Abstract

We propose a version of the quantum ergodicity theorem on large regular graphs of fixed valency. This is a property of delocalization of “most” eigenfunctions. We consider expander graphs with few short cycles (for instance random large regular graphs). Our method mimics the proof of quantum ergodicity on manifolds: it uses microlocal analysis on regular trees, as introduced by the second author in an earlier paper.
Original languageEnglish
Pages (from-to)723-765
Number of pages43
JournalDuke Mathematical Journal
Volume164
Issue number4
Early online date16 Mar 2015
DOIs
Publication statusE-pub ahead of print - 16 Mar 2015

Bibliographical note

Acceptance date is provisional and based on date of publication.

Keywords

  • large random graphs
  • Laplacian eigenfunctions
  • quantum ergodicity
  • semiclassical measures

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