Spiders in random environment
Christophe Gallesco, Sebastian Muller, Serguei Popov, Marina, Vachkovskaia

TL;DR
This paper investigates the movement speed of a multi-particle 'spider' in a one-dimensional random environment, showing that the spider's speed is positive or zero depending on the ratio of environment parameter to number of particles.
Contribution
It establishes a phase transition in the spider's speed based on the ratio of environment parameter to the number of particles, extending understanding of RWRE dynamics.
Findings
Spider speed is positive if ppa/N > 1.
Spider speed is zero if ppa/N < 1.
Single RWRE has positive speed, unlike the spider when ppa/N < 1.
Abstract
A spider consists of several, say , 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 as underlying random walk. We suppose the environment to be elliptic, with positive drift and nestling, so that there exists a unique positive constant such that . 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 and null if . In particular, if a spider has null speed but the speed of a (single) RWRE is positive.
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