Pseudo-differential calculus and quantum ergodicity on regular graphs

I will present a quantum ergodicity theorem on large regular graphs.
This is a result of spatial equidistribution of most eigenfunctions of the discrete Laplacian
in the limit of large regular graphs. It is analogous to the quantum ergodicity theorem on
Riemannian manifolds, which is concerned with the eigenfunctions of the Laplace-Beltrami operator
in the high frequency limit. I will also talk about pseudo-differential calculus on regular graphs,
one of the tools constructed for the proof of the theorem.

This is a joint work with Nalini Anantharaman.