Quantum ergodicity on large regular graphs

Nalini Anantharaman (1, 2) , Etienne Le Masson (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 IRMA - Institut de Recherche Mathématique Avancée

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.

Mots clés: large random graphs; laplacian eigenfunctions; quantum ergodicity; semiclassical measures

Domaines: Physique mathématique [math-ph]; Probabilités [math.PR]; Théorie spectrale [math.SP]

Nalini Anantharaman, Etienne Le Masson. Quantum ergodicity on large regular graphs. 2013. ⟨hal-00813596v2⟩