A counterexample to monotonicity of relative mass in random walks
نویسندگان
چکیده
For a finite undirected graph G = (V, E), let pu,v(t) denote the probability that a continuoustime 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 ru,v(t) = pu,v(t) pu,u(t) t ≥ 0 is not monotonically non-decreasing. This answers a question asked by Peres in 2013.
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