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2015 Choices, intervals and equidistribution
Matthew Junge
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Electron. J. Probab. 20: 1-18 (2015). DOI: 10.1214/EJP.v20-4191


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.


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Matthew Junge. "Choices, intervals and equidistribution." Electron. J. Probab. 20 1 - 18, 2015.


Accepted: 16 September 2015; Published: 2015
First available in Project Euclid: 4 June 2016

zbMATH: 1338.60132
MathSciNet: MR3399833
Digital Object Identifier: 10.1214/EJP.v20-4191

Primary: Probability

Vol.20 • 2015
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