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 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