The Annals of Probability

Ballistic random walks in random environment at low disorder

Christophe Sabot

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Abstract

We consider random walks in a random environment of the type p0+γξz, where p0 denotes the transition probabilities of a stationary random walk on ℤd, to nearest neighbors, and ξz is an i.i.d. random perturbation. We give an explicit expansion, for small γ, of the asymptotic speed of the random walk under the annealed law, up to order 2. As an application, we construct, in dimension d≥2, a walk which goes faster than the stationary walk under the mean environment.

Article information

Source
Ann. Probab., Volume 32, Number 4 (2004), 2996-3023.

Dates
First available in Project Euclid: 8 February 2005

Permanent link to this document
https://projecteuclid.org/euclid.aop/1107883345

Digital Object Identifier
doi:10.1214/009117904000000739

Mathematical Reviews number (MathSciNet)
MR2094437

Zentralblatt MATH identifier
1063.60149

Subjects
Primary: 60K37: Processes in random environments
Secondary: 82D30: Random media, disordered materials (including liquid crystals and spin glasses) 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)

Keywords
Random walks random media random walks in random environment Green functions

Citation

Sabot, Christophe. Ballistic random walks in random environment at low disorder. Ann. Probab. 32 (2004), no. 4, 2996--3023. doi:10.1214/009117904000000739. https://projecteuclid.org/euclid.aop/1107883345


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