Behavior of random walk on discrete point processes

TL;DR

This paper studies random walks on a specific type of random environment in Z^d, characterizing when they are transient or recurrent and proving a CLT under certain conditions.

Contribution

It provides a partial characterization of transience and recurrence, and establishes a CLT for these random walks under a new distance condition.

Findings

Partial characterization of transience and recurrence in different dimensions

Proof of CLT under a specific distance condition

Insights into behavior of random walks 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.