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arXiv · 1508.05423

Transience in growing subgraphs via evolving sets

Amir Dembo·Ruojun Huang·Ben Morris·Yuval Peres
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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].

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Amir Dembo, Ruojun Huang, Ben Morris, Yuval Peres. 2015-08-21. Transience in growing subgraphs via evolving sets. https://arxiv.org/abs/1508.05423

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