Quantum Ergodicity and Mixing on Large Schreier Graphs

In this talk, I will present joint work with Charles Bordenave and Mostafa Sabri establishing quantum ergodicity and quantum weak mixing for sequences of finite Schreier graphs converging, in the Benjamini–Schramm sense, to an infinite Cayley graph whose adjacency operator has absolutely continuous spectrum. The proof relies on a new approach to quantum ergodicity on graphs, based on trace computations, resolvent approximations and representation theory.