Spiders in random environment

@article{Gallesco2010SpidersIR,
  title={Spiders in random environment},
  author={Christophe Gallesco and Sebastian Muller and Serguei Yu. Popov and M. Vachkovskaia},
  journal={arXiv: Probability},
  year={2010}
}
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… 
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