Asymptotic analysis of random walks on ice and graphite

TL;DR

This paper analyzes the long-term behavior of random walks on ice and graphite crystal structures, establishing laws of large numbers and normality using martingale asymptotics.

Contribution

It provides the first rigorous asymptotic analysis of random walks on specific 3D crystal lattices, focusing on ice and graphite structures.

Findings

Proved strong law of large numbers for random walks on ice and graphite.

Established asymptotic normality for these random walks.

Utilized multi-dimensional martingale techniques for analysis.

Abstract

The purpose of this paper is to investigate the asymptotic behavior of random walks on three-dimensional crystal structures. We focus our attention on the 1h structure of the ice and the 2h structure of graphite. We establish the strong law of large numbers and the asymptotic normality for both random walks on ice and graphite. All our analysis relies on asymptotic results for multi-dimensional martingales.