Publication

Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds

Matthew De Courcy-Ireland
2021
Journal Articles

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.

Official source

https://infoscience.epfl.ch/entities/publication/34df0359-b2a2-40d2-8637-78104e4e7307

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Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds

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