Discrete low-discrepancy sequences

Details Discrete low-discrepancy sequences Discrete low-discrepancy sequences

2009-10-06

arxiv.org/abs/0910.1077v3

Mathematics

Combinatorics

Since posting the preprint, we have learned that our main result was proved by Tijdeman in the 1970s and that his proof is the

Scientific paper

Holroyd and Propp used Hall's marriage theorem to show that, given a probability distribution pi on a finite set S, there exists an infinite sequence s_1,s_2,... in S such that for all integers k >= 1 and all s in S, the number of i in [1,k] with s_i = s differs from k pi(s) by at most 1. We prove a generalization of this result using a simple explicit algorithm. A special case of this algorithm yields an extension of Holroyd and Propp's result to the case of discrete probability distributions on infinite sets.

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