Cutpoints for Random Walks on Quasi-Transitive Graphs
Probability
2017-12-08 v1
Abstract
We prove that a simple random walk on quasi-transitive graphs with the volume growth being faster than any polynomial of degree 4 has a.s. infinitely many cut times, and hence infinitely many cutpoints. This confirms a conjecture raised by I. Benjamini, O. Gurel-Gurevich and O. Schramm [2011, Cutpoints and resistance of random walk paths, {\it Ann. Probab.} {\bf 39(3)}, 1122-1136] that PATH of simple random walk on any transient vertex-transitive graph has a.s. infinitely many cutpoints in the corresponding case.
Cite
@article{arxiv.1712.02543,
title = {Cutpoints for Random Walks on Quasi-Transitive Graphs},
author = {He Song and Kainan Xiang},
journal= {arXiv preprint arXiv:1712.02543},
year = {2017}
}