Random walks on the two-dimensional K-comb lattice

TL;DR

This paper investigates the behavior of symmetric random walks on generalized two-dimensional comb lattices, extending the classical comb structure to include multiple horizontal lines, and analyzes their path properties.

Contribution

It introduces a generalized comb lattice model with multiple horizontal lines and studies the path behavior of symmetric random walks on these structures.

Findings

Characterization of the walk's path behavior on generalized comb lattices

Extension of classical comb lattice results to multiple horizontal lines

Insights into the diffusive properties of the walk on these structures

Abstract

We study the path behavior of the symmetric walk on some special comb-type subsets of ${\mathbb Z}^2$ which are obtained from ${\mathbb Z}^2$ by generalizing the comb having finitely many horizontal lines instead of one.