DAN

Abstract

This will be a (non exhaustive) survey talk about the behaviour of eigenfunctions of the laplacian on a compact manifold, in the asymptotic regime where the eigenvalue goes to infinity. The issue of ``quantum ergodicity'' is to understand the places where the eigenfunctions can concentrate. Recently, there has been increasing interest about possible analogues for the discrete laplacian on finite graphs (for instance, with the work of Brooks and Lindenstrauss). According to the physics literature, the interesting asymptotic regime to look at is the case of families of graphs whose size goes to infinity. As far as graphs are concerned, the talk will contain more open questions than results.