Electronic Communications in Probability

Avoidance Coupling

Omer Angel, Alexander Holroyd, James Martin, Peter Winkler, and David Wilson

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We examine the question of whether a collection of random walks on a graph can be coupled so that they never collide.  In particular, we show that on the complete graph on n vertices, with or without loops, there is a Markovian coupling keeping apart Omega(n/log n) random walks, taking turns to move in discrete time.

Article information

Electron. Commun. Probab., Volume 18 (2013), paper no. 58, 13 pp.

Accepted: 9 July 2013
First available in Project Euclid: 7 June 2016

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Zentralblatt MATH identifier

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

coupling coloring

This work is licensed under a Creative Commons Attribution 3.0 License.


Angel, Omer; Holroyd, Alexander; Martin, James; Winkler, Peter; Wilson, David. Avoidance Coupling. Electron. Commun. Probab. 18 (2013), paper no. 58, 13 pp. doi:10.1214/ECP.v18-2275. https://projecteuclid.org/euclid.ecp/1465315597

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