Choices, intervals and equidistribution. (English) Zbl 1338.60132

Summary: 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 (cf.[P. Maillard and E. Paquette, Discrete Math. Theor. Comput. Sci. (DMTCS-HAL), Proceedings BA, 289–300 (2014; Zbl 1332.62275); Isr. J. Math. 212, No. 1, 337–384 (2016; doi:10.1007/s11856-016-1289-6)]).


60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60J05 Discrete-time Markov processes on general state spaces
60G70 Extreme value theory; extremal stochastic processes


Zbl 1332.62275
Full Text: DOI arXiv