arXiv subjects

Fabien Montégut

Publications and source records attributed to Fabien Montégut.

2 recordsLinked to original sources

arXiv2021

Asymptotic analysis of random walks on ice and graphite

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.

math-ph↗

arXiv2019

Double asymptotic for random walks on hypercubes

We consider the sum of the coordinates of a simple random walk on the K-dimensional hypercube, and prove a double asymptotic of this process, as both the time parameter n and the space parameter K tend to infinity. Depending on the asymptotic ratio of the two parameters, they converge towards either a Brownian motion, an Ornstein-Uhlenbeck process or an i.i.d. collection of Gaussian variables.

math.PR↗