Choices, intervals and equidistribution

Abstract

We give a sufficient condition for a random sequence in [0,1] generated by a Psi-process to be equidistributed. The condition is met by the canonical example - the max-2 process - where the $n$th term is whichever of two uniformly placed points falls in the larger gap formed by the previous $n$-1 points. Also, we deduce equidistribution for an interpolation of the min-2 and max-2 processes that is biased towards min-2, as well as more general interpolations. This solves an open problem from Itai Benjamini, Pascal Maillard and Elliot Paquette.