From quantum ergodicity to random waves on manifolds and graphs
Evan Williams theatre
T: 03 8344 7887
The Quantum ergodicity theorem is a result of delocalisation of eigenfunctions of the Laplacian on manifolds, valid in ergodic dynamical settings. We will give a gentle introduction to this result and to the Quantum Unique Ergodicity conjecture of Rudnick and Sarnak, formulated in 1994. We will then explore the interactions between eigenfunctions on manifolds and graphs with a quick overview of recent results in collaboration with N. Anantharaman, S. Brooks and E. Lindenstrauss. Inspired by the theory on graphs, we will then introduce a new perspective in the quantum ergodicity theory on manifolds associated with the notion of Benjamini-Schramm limit (joint with T. Sahlsten) and show how this new setting connects to the 40 year old random wave conjecture of Berry.
Dr Etienne Le Masson, University of Bristol