Asymptotic analysis of random walks on ice and graphite

Bernard Bercu (1) , Fabien Montégut (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Mots clés: Random walk; Hexagonal lattice; Central limit theorem

Domaines: Probabilités [math.PR]; Physique mathématique [math-ph]

Bernard Bercu, Fabien Montégut. Asymptotic analysis of random walks on ice and graphite. Journal of Mathematical Physics, In press. ⟨hal-03347046⟩