Local weak limits of Laplace eigenfunctions
Local weak limits of Laplace eigenfunctions
In this paper, we introduce a new notion of convergence for the Laplace eigenfunctions in the semiclassical limit, the local weak convergence.This allows us to give a rigorous statement of Berry's random wave conjecture.Using recent results of Bourgain, Buckley and Wigman, we will prove that some deterministic families of eigenfunctions …