### 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) |
---|---|

Article number | 8 |

Journal | Electronic Communications in Probability |

Volume | 21 |

DOIs | |

State | Published - 2016 |

### Fingerprint

### Keywords

- Continuous-time random walk
- Lamplighter graph

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*Electronic Communications in Probability*,

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

**A counterexample to monotonicity of relative mass in random walks.** / Regev, Oded; Shinkar, Igor.

Research output: Contribution to journal › Article

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

}

TY - JOUR

T1 - A counterexample to monotonicity of relative mass in random walks

AU - Regev, Oded

AU - Shinkar, Igor

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Continuous-time random walk

KW - Lamplighter graph

UR - http://www.scopus.com/inward/record.url?scp=84964322480&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84964322480&partnerID=8YFLogxK

U2 - 10.1214/16-ECP4392

DO - 10.1214/16-ECP4392

M3 - Article

VL - 21

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

SN - 1083-589X

M1 - 8

ER -