Random walk on discrete point processes

Details Random walk on discrete point processes Random walk on discrete point processes

2010-05-09

arxiv.org/abs/1005.1398v2

Mathematics

Probability

44 pages, one figure. This is R. Rosenthal's Masters thesis. Advisor: Noam Berger

Scientific paper

We consider a model for random walks on random environments (RWRE) with random subset of the d-dimensional Euclidean lattice as the vertices, and uniform transition probabilities on 2d points (two "coordinate nearest points" in each of the d coordinate directions). We prove that the velocity of such random walks is almost surely 0, and give partial characterization of transience and recurrence for the different dimensions. Finally we prove Central Limit Theorem for such random walks, under a condition on the distance between nearest coordinate nearest points.

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