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SMALL-SCALE EQUIDISTRIBUTION OF RANDOM WAVES GENERATED BY AN UNFAIR COIN FLIP
Part of:
Spectral theory and eigenvalue problems
Partial differential equations on manifolds; differential operators
Probability theory on algebraic and topological structures
Published online by Cambridge University Press: 29 November 2021
Abstract
In this paper we study the small-scale equidistribution property of random waves whose coefficients are determined by an unfair coin. That is, the coefficients take value
$+1$
with probability p and
$-1$
with probability
$1-p$
. Random waves whose coefficients are associated with a fair coin are known to equidistribute down to the wavelength scale. We obtain explicit requirements on the deviation from the fair (
$p=0.5$
) coin to retain equidistribution.
Keywords
- Type
- Research Article
- Information
- Copyright
- © The Author(s), 2021. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.
Footnotes
Communicated by Nathan Ross
The first author was supported by the University of Auckland’s Summer Scholar Scheme.
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