1304.4343 (Nalini Anantharaman et al.)

Quantum ergodicity on large regular graphs    [PDF]

Nalini Anantharaman, Etienne Le Masson

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.

View original: http://arxiv.org/abs/1304.4343