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Monotonicity of Avoidance Coupling on KN

Part of: Markov processes

Published online by Cambridge University Press:  03 June 2016

OHAD N. FELDHEIM
OHAD N. FELDHEIM*
Affiliation:
Department of Mathematics, Stanford University, Stanford, CA 94305, USA (e-mail: [email protected])
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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.

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 26 , Issue 1 , January 2017 , pp. 16 - 23
Copyright
Copyright © Cambridge University Press 2016 

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References

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