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2019 An invariance principle for one-dimensional random walks among dynamical random conductances
Marek Biskup
Electron. J. Probab. 24: 1-29 (2019). DOI: 10.1214/19-EJP348

Abstract

We study variable-speed random walks on $\mathbb{Z} $ driven by a family of nearest-neighbor time-dependent random conductances $\{a_{t}(x,x+1)\colon x\in \mathbb{Z} ,\,t\ge 0\}$ whose law is assumed invariant and ergodic under space-time shifts. We prove a quenched invariance principle for the random walk under the minimal moment conditions on the environment; namely, assuming only that the conductances possess the first positive and negative moments. A novel ingredient is the representation of the parabolic coordinates and the corrector via a dual random walk which is considerably easier to analyze.

Citation

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Marek Biskup. "An invariance principle for one-dimensional random walks among dynamical random conductances." Electron. J. Probab. 24 1 - 29, 2019. https://doi.org/10.1214/19-EJP348

Information

Received: 25 March 2019; Accepted: 27 July 2019; Published: 2019
First available in Project Euclid: 10 September 2019

zbMATH: 07107394
MathSciNet: MR4003140
Digital Object Identifier: 10.1214/19-EJP348

Subjects:
Primary: 60K37, 74Q10, 82C41

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Vol.24 • 2019
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