Monotonicity of Avoidance Coupling on KN

Ohad N. Feldheim*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Answering a question by Angel, Holroyd, Martin, Wilson and Winkler [1], we show that the maximal number of non-colliding coupled simple random walks on the complete graph KN, which take turns, moving one at a time, is monotone in N. We use this fact to couple [N/4] such walks on KN, improving the previous Ω(N/log N) lower bound of Angel et al. We also introduce a new generalization of simple avoidance coupling which we call partially ordered simple avoidance coupling, and provide a monotonicity result for this extension as well.

Original languageAmerican English
Pages (from-to)16-23
Number of pages8
JournalCombinatorics Probability and Computing
Volume26
Issue number1
DOIs
StatePublished - 1 Jan 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2016 Cambridge University Press.

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