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March 2018 Scaling limits for sub-ballistic biased random walks in random conductances
Alexander Fribergh, Daniel Kious
Ann. Probab. 46(2): 605-686 (March 2018). DOI: 10.1214/16-AOP1159

Abstract

We consider biased random walks in positive random conductances on the $d$-dimensional lattice in the zero-speed regime and study their scaling limits. We obtain a functional law of large numbers for the position of the walker, properly rescaled. Moreover, we state a functional central limit theorem where an atypical process, related to the fractional kinetics, appears in the limit.

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Alexander Fribergh. Daniel Kious. "Scaling limits for sub-ballistic biased random walks in random conductances." Ann. Probab. 46 (2) 605 - 686, March 2018. https://doi.org/10.1214/16-AOP1159

Information

Received: 1 January 2016; Revised: 1 September 2016; Published: March 2018
First available in Project Euclid: 9 March 2018

zbMATH: 06864071
MathSciNet: MR3773372
Digital Object Identifier: 10.1214/16-AOP1159

Subjects:
Primary: 60K37
Secondary: 82D30

Keywords: Random conductances , Random walks in random environments , Scaling limit , Trap model , zero-speed

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.46 • No. 2 • March 2018
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