Choices, intervals and equidistribution

Matthew Junge
2015 Electronic Journal of Probability  
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 for
more » ... quidistribution for more general Ψ-processes. This includes an interpolation of the min-2 and max-2 processes that is biased towards min-2. t has similar properties as those needed of A t to deduce convergence in [MP14] . We then use this to establish Theorem 1. Section 4 contains the proofs for the previous section. Finally, in Section 5 we prove Corollary 2 by showing that various interpolations satisfy (1.1).
doi:10.1214/ejp.v20-4191 fatcat:pqyvw3il25fhvbe7nrtdmddyli