Behavior of random walk on discrete point processes

Abstract

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

33 pages, 3 figures, this is the article version of the masters thesis of the second author, appearing at arXiv:1005.1398

References in corpus (4)

• Random walks on supercritical percolation clusters
• Anomalous heat-kernel decay for random walk among bounded random conductances
• Lingering random walks in random environment on a strip
• Random walk on discrete point processes

Cited by in corpus (5)

• Random walks in a one-dimensional Lévy random environment
• Einstein relation for random walks in random environment
• Large fluctuations and transport properties of the Lévy-Lorentz gas
• Ladder costs for random walks in Lévy random media
• Quenched invariance principle for simple random walk on discrete point processes