Spiders in random environment

Abstract

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)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 is an element of Z) to be elliptic, with positive drift and nestling, so that there exists a unique positive constant kappa 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 kappa/N > 1 and null if kappa/N < 1. In particular, if kappa/N < 1 a spider has null speed but the speed of a (single) RWRE is positive.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 ra8129147CAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL DE NÍVEL SUPERIORCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)FAPESP [2009/51139-3, 2009/08665-6]DFG [MU 2868/1-1]CNPq [300886/2008-0, 472431/2009-9, 304561/2006-1]SEM INFORMAÇÃO300886/2008–0; 472431/2009–9; 304561/2006–12009/51139-3; 2009/08665-