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2020 Green kernel asymptotics for two-dimensional random walks under random conductances
Sebastian Andres, Jean-Dominique Deuschel, Martin Slowik
Electron. Commun. Probab. 25: 1-14 (2020). DOI: 10.1214/20-ECP337

Abstract

We consider random walks among random conductances on $\mathbb {Z}^{2}$ and establish precise asymptotics for the associated potential kernel and the Green’s function of the walk killed upon exiting balls. The result is proven for random walks on i.i.d. supercritical percolation clusters among ergodic degenerate conductances satisfying a moment condition. We also provide a similar result for the time-dynamic random conductance model. As an application we present a scaling limit for the variances in the Ginzburg-Landau $\nabla \phi $-interface model.

Citation

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Sebastian Andres. Jean-Dominique Deuschel. Martin Slowik. "Green kernel asymptotics for two-dimensional random walks under random conductances." Electron. Commun. Probab. 25 1 - 14, 2020. https://doi.org/10.1214/20-ECP337

Information

Received: 19 December 2019; Accepted: 9 July 2020; Published: 2020
First available in Project Euclid: 8 August 2020

zbMATH: 07252778
MathSciNet: MR4137943
Digital Object Identifier: 10.1214/20-ECP337

Subjects:
Primary: 39A12, 60J35, 60J45, 60K37, 82C41

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