Shrinking scale equidistribution for monochromatic random waves on compact manifolds

DOI10.1093/IMRN/RNAA042arXiv1902.05271MaRDI QIDQ6314061

Publication date: 14 February 2019

Abstract: We prove equidistribution at shrinking scales for the monochromatic ensemble on a compact Riemannian manifold of any dimension. This ensemble on an arbitrary manifold takes a slowly growing spectral window in order to synthesize a random function. With high probability, equidistribution takes place close to the optimal wave scale and simultaneously over the whole manifold. The proof uses Weyl's law to approximate the two-point correlation function of the ensemble, and a Chernoff bound to deduce concentration.

Mathematics Subject Classification ID

Quantum optics (81V80) Axiomatic quantum field theory; operator algebras (81T05) Local Riemannian geometry (53B20) Traveling wave solutions (35C07)

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