Quantum unique ergodicity for random bases of spectral projections

TL;DR

This paper demonstrates that random wave models on Riemannian manifolds typically exhibit quantum unique ergodicity, indicating uniform distribution of eigenfunctions in the high-energy limit, under mild conditions.

Contribution

It proves that random waves satisfy quantum unique ergodicity with probability one, advancing understanding of eigenfunction behavior on manifolds.

Findings

Random waves satisfy quantum unique ergodicity with probability one.

The proof uses the exponential moment method under mild growth assumptions.

Supports the typicality of ergodic eigenfunction distribution in spectral theory.

Abstract

We consider a random wave model introduced by Zelditch to study the behavior of typical quasi-modes on a Riemannian manifold. Using the exponential moment method, we show that random waves satisfy the quantum unique ergodicity property with probability one under mild growth assumptions.