@article{1e7ab7d1fe7e42e1901645d6f0c9f695,

title = "A counterexample to monotonicity of relative mass in random walks",

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.",

keywords = "Continuous-time random walk, Lamplighter graph",

author = "Oded Regev and Igor Shinkar",

note = "Funding Information: The first author{\textquoteright}s research is supported by the Simons Collaboration on Algorithms and Geometry and by the National Science Foundation (NSF) under Grant No. CCF-1320188. The second author{\textquoteright}s research is supported by NSF grants CCF 1422159, 1061938, 0832795 and Simons Collaboration on Algorithms and Geometry grant. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF. Publisher Copyright: {\textcopyright} 2016, University of Washington. All rights reserved.",

year = "2016",

doi = "10.1214/16-ECP4392",

language = "English (US)",

volume = "21",

journal = "Electronic Communications in Probability",

issn = "1083-589X",

publisher = "Institute of Mathematical Statistics",

}