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E l e c t r o n i c J o u r n a l o f P r o b a b i l i t y Electron. Abstract We give a sufficient condition for a random sequence in [0,1] generated by a Ψprocess to be equidistributed. The condition is met by the canonical example -the max-2 process -where the nth term is whichever of two uniformly placed points falls in the larger gap formed by the previous n − 1 points. This solves an open problem from Itai Benjamini, Pascal Maillard and Elliot Paquette. We also deduce equidistribution fordoi:10.1214/ejp.v20-4191 fatcat:pqyvw3il25fhvbe7nrtdmddyli