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2016 Stability and instability of Gaussian heat kernel estimates for random walks among time-dependent conductances
Ruojun Huang, Takashi Kumagai
Electron. Commun. Probab. 21: 1-11 (2016). DOI: 10.1214/15-ECP4347

Abstract

We consider time-dependent random walks among time-dependent conductances. For discrete time random walks, we show that, unlike the time-independent case, two-sided Gaussian heat kernel estimates are not stable under perturbations. This is proved by giving an example of a ballistic and transient time-dependent random walk on $\mathbb{Z}$ among uniformly elliptic time-dependent conductances. For continuous time random walks, we show the instability when the holding times are i.i.d. $\exp(1)$, and in contrast, we prove the stability when the holding times change by sites in such a way that the base measure is a uniform measure.

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Ruojun Huang. Takashi Kumagai. "Stability and instability of Gaussian heat kernel estimates for random walks among time-dependent conductances." Electron. Commun. Probab. 21 1 - 11, 2016. https://doi.org/10.1214/15-ECP4347

Information

Received: 6 June 2015; Accepted: 18 December 2015; Published: 2016
First available in Project Euclid: 3 February 2016

zbMATH: 1338.60196
MathSciNet: MR3485374
Digital Object Identifier: 10.1214/15-ECP4347

Subjects:
Primary: 60J35
Secondary: 60J05, 60J25, 60J45

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