Duke Mathematical Journal
- Duke Math. J.
- Volume 164, Number 4 (2015), 723-765.
Quantum ergodicity on large regular graphs
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.
Duke Math. J., Volume 164, Number 4 (2015), 723-765.
First available in Project Euclid: 16 March 2015
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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