Monotonicity of Avoidance Coupling on KN

Ohad N. Feldheim

doi:https://doi.org/10.1017/S0963548316000195

Monotonicity of Avoidance Coupling on K_N

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	16-23
Number of pages	8
Journal	Combinatorics Probability and Computing
Volume	26
Issue number	1
DOIs	https://doi.org/10.1017/S0963548316000195
State	Published - 1 Jan 2017
Externally published	Yes

All Science Journal Classification (ASJC) codes

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

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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.",

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JO - Combinatorics Probability and Computing

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Monotonicity of Avoidance Coupling on K_N

Abstract

All Science Journal Classification (ASJC) codes

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