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January 2020 Quenched invariance principle for random walks among random degenerate conductances
Peter Bella, Mathias Schäffner
Ann. Probab. 48(1): 296-316 (January 2020). DOI: 10.1214/19-AOP1361

Abstract

We consider the random conductance model in a stationary and ergodic environment. Under suitable moment conditions on the conductances and their inverse, we prove a quenched invariance principle for the random walk among the random conductances. The moment conditions improve earlier results of Andres, Deuschel and Slowik (Ann. Probab. 43 (2015) 1866–1891) and are the minimal requirement to ensure that the corrector is sublinear everywhere. The key ingredient is an essentially optimal deterministic local boundedness result for finite difference equations in divergence form.

Citation

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Peter Bella. Mathias Schäffner. "Quenched invariance principle for random walks among random degenerate conductances." Ann. Probab. 48 (1) 296 - 316, January 2020. https://doi.org/10.1214/19-AOP1361

Information

Received: 1 February 2019; Revised: 1 March 2019; Published: January 2020
First available in Project Euclid: 25 March 2020

zbMATH: 07206759
MathSciNet: MR4079437
Digital Object Identifier: 10.1214/19-AOP1361

Subjects:
Primary: 60F17, 60K37, 82C41

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 1 • January 2020
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