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.
Bibliographical noteAcceptance date is provisional and based on date of publication.
- large random graphs
- Laplacian eigenfunctions
- quantum ergodicity
- semiclassical measures