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FELDHEIM, OHAD N.
Combinatorics, probability & computing, 01/2017, Volume: 26, Issue: 1Journal Article
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.
