Electronic Journal of Probability
- Electron. J. Probab.
- Volume 20 (2015), paper no. 97, 18 pp.
Choices, intervals and equidistribution
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.
Electron. J. Probab., Volume 20 (2015), paper no. 97, 18 pp.
Accepted: 16 September 2015
First available in Project Euclid: 4 June 2016
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Junge, Matthew. Choices, intervals and equidistribution. Electron. J. Probab. 20 (2015), paper no. 97, 18 pp. doi:10.1214/EJP.v20-4191. https://projecteuclid.org/euclid.ejp/1465067203