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Article Dans Une Revue ALEA : Latin American Journal of Probability and Mathematical Statistics Année : 2011

Spiders in random environment

Résumé

A spider consists of several, say N, particles. Particles can jump independently according to a random walk if the movement does not violate some given restriction rules. If the movement violates a rule it is not carried out. We consider random walk in random environment (RWRE) on $\Z$ as underlying random walk. We suppose the environment $\omega=(\omega_x)_{x \in \Z}$ to be elliptic, with positive drift and nestling, so that there exists a unique positive constant κ such that $\E[((1-\omega_0)/\omega_0)^{\kappa}]=1$. The restriction rules are kept very general; we only assume transitivity and irreducibility of the spider. The main result is that the speed of a spider is positive if κ/N>1 and null if κ/N<1. In particular, if κ/N<1 a spider has null speed but the speed of a (single) RWRE is positive.

Dates et versions

hal-01255367 , version 1 (13-01-2016)

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Christophe Gallesco, Sebastian Mueller, Serguei Popov, Marina Vachkovskaia. Spiders in random environment. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2011, 8, pp.127-147. ⟨hal-01255367⟩

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