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Small-Scale Equidistribution of Random Waves Generated by an Unfair Coin Flip
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.
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