Ballistic random walks in random environment at low disorder

2003/02/28 by Christophe Sabot
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Diffusion and Search Dynamics #Stochastic processes and statistical mechanics #math.PR #msc:60K37 #stochastic dynamics and bifurcation

paper · pdf · doi:10.1214/009117904000000739

published as Annals of Probability 2004, Vol. 32, No. 4, 2996-3023 · Published at http://dx.doi.org/10.1214/009117904000000739 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

openalex publication_date 2004/10/01 · arxiv created 2005/04/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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