Asymptotic analysis of random walks on ice and graphite

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.