### 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 ε 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.

Original language | English (US) |
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Article number | 8 |

Journal | Electronic Communications in Probability |

Volume | 21 |

DOIs | |

State | Published - 2016 |

### Keywords

- Continuous-time random walk
- Lamplighter graph

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

Regev, O., & Shinkar, I. (2016). A counterexample to monotonicity of relative mass in random walks.

*Electronic Communications in Probability*,*21*, [8]. https://doi.org/10.1214/16-ECP4392