An Upper Bound on the Size of Avoidance Couplings-Reference-Cited by-同舟云学术

An Upper Bound on the Size of Avoidance Couplings

Published:2018-12-11 Issue:3 Volume:28 Page:325-334
ISSN:0963-5483
Container-title:Combinatorics, Probability and Computing
language:en
Short-container-title:Combinator. Probab. Comp.

Author:

BATES ERIK,SAUERMANN LISA

Abstract

We show that a coupling of non-colliding simple random walkers on the complete graph on n vertices can include at most n - log n walkers. This improves the only previously known upper bound of n - 2 due to Angel, Holroyd, Martin, Wilson and Winkler (Electron. Commun. Probab.18 (2013)). The proof considers couplings of i.i.d. sequences of Bernoulli random variables satisfying a similar avoidance property, for which there is separate interest.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science

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