Random walk on comb-type subsets of Z^2

TL;DR

This paper investigates the behavior of simple symmetric random walks on specialized comb-like subsets of the two-dimensional integer lattice, providing strong approximation results and exploring their implications.

Contribution

It introduces a new class of comb-type subsets of Z^2 and analyzes the path behavior of random walks on these structures, offering novel approximation results.

Findings

Strong approximation results for random walks on comb-type subsets

Insights into the path behavior and structure of these walks

Discussion of the implications of these results

Abstract

We study the path behavior of the simple symmetric walk on some comb-type subsets of Z^2 which are obtained from Z^2 by removing all horizontal edges belonging to certain sets of values on the y-axis. We obtain some strong approximation results and discuss their consequences.