Open Access
November 2013 Biased random walk in positive random conductances on $\mathbb{Z}^{d}$
Alexander Fribergh
Ann. Probab. 41(6): 3910-3972 (November 2013). DOI: 10.1214/13-AOP835


We study the biased random walk in positive random conductances on $\mathbb{Z}^{d}$. This walk is transient in the direction of the bias. Our main result is that the random walk is ballistic if, and only if, the conductances have finite mean. Moreover, in the sub-ballistic regime we find the polynomial order of the distance moved by the particle. This extends results obtained by Shen [Ann. Appl. Probab. 12 (2002) 477–510], who proved positivity of the speed in the uniformly elliptic setting.


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Alexander Fribergh. "Biased random walk in positive random conductances on $\mathbb{Z}^{d}$." Ann. Probab. 41 (6) 3910 - 3972, November 2013.


Published: November 2013
First available in Project Euclid: 20 November 2013

zbMATH: 1291.60209
MathSciNet: MR3161466
Digital Object Identifier: 10.1214/13-AOP835

Primary: 60K37
Secondary: 60J45

Keywords: heavy-tailed random variables , Random walk in random conductances

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.41 • No. 6 • November 2013
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