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research article

Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds

de Courcy-Ireland, Matthew  
February 1, 2021
International Mathematics Research Notices

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
DOI
10.1093/imrn/rnaa042
Web of Science ID

WOS:000630056600021

Author(s)
de Courcy-Ireland, Matthew  
Date Issued

2021-02-01

Publisher

OXFORD UNIV PRESS

Published in
International Mathematics Research Notices
Volume

2021

Issue

4

Start page

3021

End page

3055

Subjects

Mathematics

•

ergodicity

Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
TN  
Available on Infoscience
April 24, 2021
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/177499
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