Year: 2016
Type: article
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.
Author: OHAD N. FELDHEIM
Institutions: University of Minnesota, Stanford University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2231670391