Transience in growing subgraphs via evolving sets
Probability
2016-03-22 v3
Abstract
We extend the use of random evolving sets to time-varying conductance models and utilize it to provide tight heat kernel upper bounds. It yields the transience of any uniformly lazy random walk, on Z^d, d>=3, equipped with uniformly bounded above and below, independently time-varying edge conductances, of (effectively) non-decreasing in time vertex conductances (i.e. reversing measure), thereby affirming part of [ABGK, Conj. 7.1].
Cite
@article{arxiv.1508.05423,
title = {Transience in growing subgraphs via evolving sets},
author = {Amir Dembo and Ruojun Huang and Ben Morris and Yuval Peres},
journal= {arXiv preprint arXiv:1508.05423},
year = {2016}
}
Comments
25 pages