# 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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## References

SHOWING 1-10 OF 13 REFERENCES

### On slowdown and speedup of transient random walks in random environment

- Mathematics
- 2008

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…

### Random walks and electric networks

- Mathematics
- 1984

The goal will be to interpret Polya’s beautiful theorem that a random walker on an infinite street network in d-dimensional space is bound to return to the starting point when d = 2, but has a positive probability of escaping to infinity without returning to the Starting Point when d ≥ 3, and to prove the theorem using techniques from classical electrical theory.

### A NOTE ON SPIDER WALKS

- Mathematics
- 2009

Spider walks are systems of interacting particles. The particles move independently as long as their movements do not violate some given rules describing the relative position of the particles; moves…

### Molecular spiders with memory.

- BiologyPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2007

This work investigates spiders moving along a one-dimensional substrate, whose legs leave newly visited sites at a slower rate than revisited sites, and finds that the slowing down of the spider at new sites increases the diffusion coefficient and accelerates the growth of the number of visited sites.

### Limit law for transition probabilities and moderate deviations for Sinai's random walk in random environment

- Mathematics
- 2003

We consider a one-dimensional random walk in random environment in the Sinai's regime. Our main result is that logarithms of the transition probabilities, after a suitable rescaling, converge in…

### Random Walks in Random Environment

- HistoryEncyclopedia of Complexity and Systems Science
- 2009

you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal,…

### Molecular spiders in one dimension

- BiologyJournal of statistical mechanics
- 2007

Molecular spiders are synthetic biomolecular systems which have ‘legs’ made of short single-stranded segments of DNA, and for spiders with simple gait and varying number of legs the diffusion coefficient is computed; when the hopping is biased the velocity is computed.

### Lecture notes on random walks in random environment. volume 1837 of Lecture Notes in Math., pages 191–312

- 2004

### Lectures on Finite Markov Chains. Lectures on probability theory and statistics (Saint-Flour

- Lecture Notes in Math.,
- 1997