Choices, intervals and equidistribution

Matthew Junge

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arXiv · 1410.6537

Choices, intervals and equidistribution

Matthew Junge

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Abstract

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. This solves an open problem from Itai Benjamini, Pascal Maillard and Elliot Paquette. We also deduce equidistribution for more general $\Psi$-processes. This includes an interpolation of the $\min$-2 and $\max$-2 processes that is biased towards $\min$-2.

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Matthew Junge. 2014-10-24. Choices, intervals and equidistribution. https://arxiv.org/abs/1410.6537

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