The Annals of Probability

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

Alexander Fribergh

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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

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

First available in Project Euclid: 20 November 2013

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Zentralblatt MATH identifier

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

Random walk in random conductances heavy-tailed random variables


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.

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