A counterexample to monotonicity of relative mass in random walks

Oded Regev, Igor Shinkar

Research output: Contribution to journalArticle

Abstract

For a finite undirected graph G = (V,E), let pu,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 ε 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.

Original languageEnglish (US)
Article number8
JournalElectronic Communications in Probability
Volume21
DOIs
StatePublished - 2016

Keywords

  • Continuous-time random walk
  • Lamplighter graph

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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