Consider a random walk {X(n) : n >= 0} in an elliptic i.i.d. environment in dimensions d >= 2 and call P(0) its averaged law starting from 0. Given a direction I is an element of S(d-1), A(l) = {lim(n ->infinity) Xn . l = ...

We prove that a law of large numbers and a central limit theorem hold for the excited random walk model in every dimension d >= 2.

In this paper we study a substantial generalization of the model of excited random walk introduced in [Electron. Commun. Probab. 8 (2003) 86-92] by Benjamini and Wilson. We consider a discrete-time stochastic process (X-n, ...

A scenery is a coloring xi of the integers. Let {S-t}(t >= 0) be a recurrent random walk on the integers. Observing the scenery xi along the path of this random walk, one sees the color chi(t) := xi(S-t) at time t. The ...

The dynamical discrete web (DyDW), introduced in the recent work of Howitt and Warren, is a system of coalescing simple symmetric one-dimensional random walks which evolve in an extra continuous dynamical time parameter ...

We consider an interacting particle system on the one-dimensional lattice Z modeling combustion. The process depends on two integer parameters 2 <= a <= M <= infinity. Particles move independently as continuous time simple ...