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.