Random walk in random environment (RWRE) is a fundamental model of statistical
mechanics, describing the movement of a particle in a highly disordered and …

We consider one-dimensional excited random walks (ERWs) with iid Markovian cookie
stacks in the non-boundary recurrent regime. We prove that under diffusive scaling such an …

In this paper we consider an excited random walk (ERW) on Z in identically piled periodic
environment. This is a discrete time process on Z defined by parameters …

We consider a nearest-neighbor random walk on Z whose probability x(j) to jump to the right
from site x depends not only on x but also on the number of prior visits j to x. The collection …

We consider one-dimensional excited random walks (ERWs) with periodic cookie stacks in
the recurrent regime. We prove functional limit theorems for these walks which extend the …

For near-critical, transient Markov chains on the non-negative integers in the Lamperti
regime, where the mean drift at x decays as 1/x as x→∞, we quantify degree of transience …

We study one dimensional excited random walks (ERW) on iterated leftover environments.
We prove a 0–1 law for directional transience and a law of large numbers for such …

We introduce a method for studying monotonicity of the speed of excited random walks in
high dimensions, based on a formula for the speed obtained via cut-times and Girsanov's …

The paper considers excited random walks (ERWs) on integers in iid environments with a
bounded number of excitations per site. The emphasis is primarily on the critical case for the …

One dimensional excited random walk has been extensively studied for bounded, iid cookie
environments. In this case, many important properties of the walk including transience or …