A counterexample to monotonicity of relative mass in random walks
ELECTRONIC COMMUNICATIONS IN PROBABILITY(2016)
摘要
For a finite undirected graph G = (V, E), let p(u,v) (t) denote the probability that a continuous-time random walk starting at vertex u is in v at time t. In this note we give an example of a Cayley graph G and two vertices u, v is an element of G for which the function r(u,v) (t) = p(u,v) (t)/p(u,u) (t) t >= 0 is not monotonically non-decreasing. This answers a question asked by Peres in 2013.
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关键词
continuous-time random walk,lamplighter graph
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