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Full-Text Articles in Physical Sciences and Mathematics
Random Walks In A Sparse Random Environment, Anastasios Matzavinos, Alexander Roitershtein, Youngsoo Seol
Random Walks In A Sparse Random Environment, Anastasios Matzavinos, Alexander Roitershtein, Youngsoo Seol
Mathematics and Statistics Faculty Publications
We introduce random walks in a sparse random environment on ℤ and investigate basic asymptotic properties of this model, such as recurrence-transience, asymptotic speed, and limit theorems in both the transient and recurrent regimes. The new model combines features of several existing models of random motion in random media and admits a transparent physical interpretation. More specifically, a random walk in a sparse random environment can be characterized as a “locally strong” perturbation of a simple random walk by a random potential induced by “rare impurities,” which are randomly distributed over the integer lattice. Interestingly, in the critical (recurrent) regime, …