Random Walk on the High-Dimensional IIC

On the Limiting Velocity of High-dimensional Random Walk in Random Environment

We show that Random Walk in uniformly elliptic i.i.d. environment in dimension ≥ 5 has at most one non-zero limiting velocity. In particular this proves a law of large numbers in the distributionally symmetric case and establishes connections between different conjectures.

Random walk on a two-dimensional random environment

Two-dimensional quantum random walk

We analyze several families of two-dimensional quantum random walks. The feasible region (the region where probabilities do not decay exponentially with time) grows linearly with time, as is the case with one-dimensional QRW. The limiting shape of the feasible region is, however, quite different. The limit region turns out to be an algebraic set, which we characterize as the rational image of a...

Erosion by a one-dimensional random walk.

We consider a model introduced by Baker et al. [Phys. Rev. E 88, 042113 (2013)] of a single lattice random walker moving on a domain of allowed sites, surrounded by blocked sites. The walker enlarges the allowed domain by eroding the boundary at its random encounters with blocked boundary sites: attempts to step onto blocked sites succeed with a given probability and convert these sites to allo...

Random walk on random walks

In this paper we study a random walk in a one-dimensional dynamic random environment consisting of a collection of independent particles performing simple symmetric random walks in a Poisson equilibrium with density ρ ∈ (0,∞). At each step the random walk performs a nearest-neighbour jump, moving to the right with probability p◦ when it is on a vacant site and probability p• when it is on an oc...