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An Upper Bound on the Size of Avoidance Couplings

Part of: Markov processes Graph theory

Published online by Cambridge University Press:  11 December 2018

ERIK BATES  and
LISA SAUERMANN
ERIK BATES
Affiliation:
Department of Mathematics, Stanford University, Stanford, CA 94305, USA (e-mail: ewbates@stanford.edu, lsauerma@stanford.edu)
LISA SAUERMANN
Affiliation:
Department of Mathematics, Stanford University, Stanford, CA 94305, USA (e-mail: ewbates@stanford.edu, lsauerma@stanford.edu)
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Abstract

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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.

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 05C81: Random walks on graphs

Information

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 28 , Issue 3 , May 2019 , pp. 325 - 334
Copyright
Copyright © Cambridge University Press 2018 

Footnotes

†

Research was partially supported by NSF grant DGE-114747.

References

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