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2016 A counterexample to monotonicity of relative mass in random walks
Oded Regev, Igor Shinkar
Electron. Commun. Probab. 21: 1-8 (2016). DOI: 10.1214/16-ECP4392

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 $u,v \in G$ for which the function \[ r_{u,v}(t) = \frac{p_{u,v}(t)} {p_{u,u}(t)} \qquad t \geq 0 \] is not monotonically non-decreasing. This answers a question asked by Peres in 2013.

Citation

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Oded Regev. Igor Shinkar. "A counterexample to monotonicity of relative mass in random walks." Electron. Commun. Probab. 21 1 - 8, 2016. https://doi.org/10.1214/16-ECP4392

Information

Received: 26 June 2015; Accepted: 21 January 2016; Published: 2016
First available in Project Euclid: 5 February 2016

zbMATH: 1343.60054
MathSciNet: MR3485377
Digital Object Identifier: 10.1214/16-ECP4392

Subjects:
Primary: 60J27

Keywords: Continuous-time random walk , lamplighter graph

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