Random walk on discrete point processes

2010/05/09 by Ron Rosenthal, Rosenthal, Ron
Mathematics · #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1005.1398

openalex publication_date 2010/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Heat Kernel Upper Bounds on Long Range Percolation Clusters
• Random walks on supercritical percolation clusters

Related

• Correlated random walk
• Universal Fluctuations in the Tail Probability for d=2 Random Walks in Space-Time Random Environments
• Random walk on random walks: higher dimensions
• Random walks in a Dirichlet environment
• Central Limit Theorem for Branching Random Walks in Random Environment