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research article
Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds
February 1, 2021
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.
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Type
research article
Web of Science ID
WOS:000630056600021
Authors
Publication date
2021-02-01
Publisher
Published in
Volume
2021
Issue
4
Start page
3021
End page
3055
Subjects
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
April 24, 2021