Duke Mathematical Journal

Quantum ergodicity on large regular graphs

Nalini Anantharaman and Etienne Le Masson

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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.

Article information

Source
Duke Math. J., Volume 164, Number 4 (2015), 723-765.

Dates
First available in Project Euclid: 16 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1426512106

Digital Object Identifier
doi:10.1215/00127094-2881592

Mathematical Reviews number (MathSciNet)
MR3322309

Zentralblatt MATH identifier
06434640

Subjects
Primary: 58J51: Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicity 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52)

Keywords
large random graphs Laplacian eigenfunctions quantum ergodicity semiclassical measures

Citation

Anantharaman, Nalini; Le Masson, Etienne. Quantum ergodicity on large regular graphs. Duke Math. J. 164 (2015), no. 4, 723--765. doi:10.1215/00127094-2881592. https://projecteuclid.org/euclid.dmj/1426512106


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