Quantum ergodicity on large regular graphs

Nalini Anantharaman; Etienne Le Masson

doi:10.1215/00127094-2881592

Quantum ergodicity on large regular graphs

Nalini Anantharaman, Etienne Le Masson

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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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 language	English
Pages (from-to)	723-765
Number of pages	43
Journal	Duke Mathematical Journal
Volume	164
Issue number	4
Early online date	16 Mar 2015
DOIs	https://doi.org/10.1215/00127094-2881592
Publication status	E-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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10.1215/00127094-2881592

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Duke University Press at https://projecteuclid.org/euclid.dmj/1426512106 . Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 498 KB

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AB - 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.

KW - large random graphs

KW - Laplacian eigenfunctions

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KW - semiclassical measures

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Quantum ergodicity on large regular graphs

Abstract

Bibliographical note

Keywords

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