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Joachim Cuntz, David Masser, Tobias Colding, Daniel Huybrechts, Jun-Muk Hwang, Olivier Schiffmann, Jakob Stix, Gábor Székelyhidi, Franz Stückle, Druck Und Verlag

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.

Locations

• Journal für die reine und angewandte Mathematik (Crelles Journal) - View - PDF