A central limit theorem for integrals of random waves-Reference-Cited by-同舟云学术

A central limit theorem for integrals of random waves

Published:2022-02-15 Issue:785 Volume:2022 Page:1-30
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

de Courcy-Ireland Matthew¹^ORCID,Lemm Marius¹^ORCID

Affiliation:

1. Institute of Mathematics , École Polytechnique Fédérale de Lausanne , SB, Station 8, CH-1015 Lausanne , Switzerland

Abstract

Abstract We derive a central limit theorem for the mean-square of random waves in the high-frequency limit over shrinking sets. Our proof applies to any compact Riemannian manifold of dimension 3 or higher, thanks to the universality of the local Weyl law. The key technical step is an estimate capturing some cancellation in a triple integral of Bessel functions, which we achieve using Gegenbauer’s addition formula.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2021-0082/pdf

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