Spiders in random environment

Author(s)

Gallesco, Christophe ^[1] ; Mueller, Sebastian ^[2] ; Popov, Serguei ^[3] ; Vachkovskaia, Marina ^[3]

Affiliation

^[1] Univ Sao Paulo, Inst Math & Stat, BR-05508090 Sao Paulo - Brazil

^[2] Univ Provence, LATP CMI, F-13453 Marseille 13 - France

^[3] Univ Campinas UNICAMP, Inst Math Stat & Sci Computat, Dept Stat, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS; v. 8, p. 129-147, 2011.
• Web of Science Citations: 4

Abstract

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. (AU)

• FAPESP's process: 09/08665-6 - Random walks on trees and branching random walks
• Grantee: Serguei Popov
• Support Opportunities: Regular Research Grants