Mathematics – Probability
Scientific paper
2010-01-14
Mathematics
Probability
25 pages, 5 figures
Scientific paper
10.1051/ps/2010008
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 $\kappa$ 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.
Gallesco Christophe
Müller Sebastian
Popov Serguei
Vachkovskaia Marina
No associations
LandOfFree
Spiders in random environment does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Spiders in random environment, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spiders in random environment will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-568673