Exact and efficient discrete random walk method for time-dependent two-dimensional environments

Title: Exact and efficient discrete random walk method for time-dependent two-dimensional environments

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Exact and efficient discrete random walk method for time-dependent two-dimensional environments.

We present an exact method for speeding up random walk in two-dimensional complicated lattice environments. To this end, we derive the discrete two-dimensional probability distribution function for a diffusing particle starting at the center of a square of linear size s. This is used to propagate random walkers from the center of the square to sites which are nearest neighbors to its perimeter ...

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...

One-dimensional discrete-time quantum walks on random environments

We consider discrete-time nearest-neighbor quantum walks on random environments in one dimension. Using the method based on a path counting, we present both quenched and annealed weak limit theorems for the quantum walk.

Random walk on a two-dimensional random environment