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1 UPN - Université Paris Nanterre

Abstract : We consider simple random walks on Delaunay triangulations generated by point processes in $\mathbb{R}^d$. Under suitable assumptions on the point processes, we show that the random walk satisfies an almost sure or quenched invariance principle. This invariance principle holds for point processes which have clustering or repulsiveness properties including Poisson point processes, Matérn cluster and Matérn hardcore processes. The method relies on the decomposition of the process into a martingale part and a corrector which is proved to be negligible at the diffusive scale.

Keywords : Delaunay triangulation 60F17 05C81 60D05 secondary: 60G55 Random walk in random environment point process quenched invariance principle isoperimetric inequalities AMS 2010 Subject Classification : Primary: 60K37

Autor: Arnaud Rousselle -

Fuente: https://hal.archives-ouvertes.fr/


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