The Annals of Probability

Biased random walk in positive random conductances on $\mathbb{Z}^{d}$

Alexander Fribergh

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Abstract

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.

Article information

Source
Ann. Probab., Volume 41, Number 6 (2013), 3910-3972.

Dates
First available in Project Euclid: 20 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.aop/1384957779

Digital Object Identifier
doi:10.1214/13-AOP835

Mathematical Reviews number (MathSciNet)
MR3161466

Zentralblatt MATH identifier
1291.60209

Subjects
Primary: 60K37: Processes in random environments
Secondary: 60J45: Probabilistic potential theory [See also 31Cxx, 31D05]

Keywords
Random walk in random conductances heavy-tailed random variables

Citation

Fribergh, Alexander. Biased random walk in positive random conductances on $\mathbb{Z}^{d}$. Ann. Probab. 41 (2013), no. 6, 3910--3972. doi:10.1214/13-AOP835. https://projecteuclid.org/euclid.aop/1384957779


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