Ballistic random walks in random environment at low disorder

2003/02/28 by Christophe Sabot
Mathematics · #math.PR #msc:60K37

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)

arxiv created 2005/04/06 · arxiv updated 2009/11/30

Abstract

We consider random walks in a random environment of the type p₀+γξ_z, where p₀ denotes the transition probabilities of a stationary random walk on \BbbZ^d, to nearest neighbors, and ξ_z 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.

Related

• Asymptotic expansion of the invariant measure for ballistic random walk\n in the low disorder regime
• Random walk in the low disorder ballistic regime
• Velocity estimates for symmetric random walks at low ballistic disorder
• Random walk on random walks: low densities
• Random walks in a Dirichlet environment