On slowdown and speedup of transient random walks in random environment

Autor(es)

Fribergh, Alexander ^[1] ; Gantert, Nina ^[2] ; Popov, Serguei ^[3]

Afiliação do(s) autor(es)

^[1] Univ Lyon 1, Univ Lyon, CNRS, Inst Camille Jordan, UMR5208, F-69622 Villeurbanne - France

^[2] Univ Munster, Inst Stat Math, Ctr Nonlinear Sci, Fachbereich Math & Informat, D-48149 Munster - Germany

^[3] Univ Sao Paulo, Inst Matemat & Estatist, BR-05508090 Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: PROBABILITY THEORY AND RELATED FIELDS; v. 147, n. 1-2, p. 43-88, MAY 2010.
• Citações Web of Science: 11

Resumo

We consider one-dimensional random walks in random environment which are transient to the right. Our main interest is in the study of the sub-ballistic regime, where at time n the particle is typically at a distance of order O(n (kappa) ) from the origin, kappa is an element of (0, 1). We investigate the probabilities of moderate deviations from this behaviour. Specifically, we are interested in quenched and annealed probabilities of slowdown (at time n, the particle is at a distance of order O (n (nu 0)) from the origin, nu(0) is an element of (0, kappa)), and speedup (at time n, the particle is at a distance of order n (nu 1) from the origin , nu(1) is an element of (kappa, 1)), for the current location of the particle and for the hitting times. Also, we study probabilities of backtracking: at time n, the particle is located around (-n (nu) ), thus making an unusual excursion to the left. For the slowdown, our results are valid in the ballistic case as well. (AU)

• Processo FAPESP: 04/07276-2 - Modelagem estocástica de sistemas interagentes
• Beneficiário: Luiz Renato Gonçalves Fontes
• Modalidade de apoio: Auxílio à Pesquisa - Temático