Quantum ergodicity on large regular graphs
Mathematical Physics
2015-11-03 v2 math.MP
Probability
Spectral Theory
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.
Keywords
Cite
@article{arxiv.1304.4343,
title = {Quantum ergodicity on large regular graphs},
author = {Nalini Anantharaman and Etienne Le Masson},
journal= {arXiv preprint arXiv:1304.4343},
year = {2015}
}
Comments
Statement of theorem 1.7 has been corrected. Some comments, remarks and references added. 30 pages