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SMALL-SCALE EQUIDISTRIBUTION OF RANDOM WAVES GENERATED BY AN UNFAIR COIN FLIP
Journal of the Australian Mathematical Society  (IF0.8),  Pub Date : 2021-11-29, DOI: 10.1017/s1446788721000185
MIRIAM J. LEONHARDT, MELISSA TACY

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.