A Counterexample to Monotonicity of Relative Mass in Random Walks

2015/06/29 by Regev, Oded, Shinkar, Igor
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1506.08631

Abstract

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 ∈ G for which the function r_u,v(t) = \fracp_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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