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2015 Quenched invariance principle for random walks on Delaunay triangulations
Arnaud Rousselle
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Electron. J. Probab. 20: 1-32 (2015). DOI: 10.1214/EJP.v20-4006

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.

Citation

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Arnaud Rousselle. "Quenched invariance principle for random walks on Delaunay triangulations." Electron. J. Probab. 20 1 - 32, 2015. https://doi.org/10.1214/EJP.v20-4006

Information

Accepted: 28 March 2015; Published: 2015
First available in Project Euclid: 4 June 2016

zbMATH: 1321.60066
MathSciNet: MR3335824
Digital Object Identifier: 10.1214/EJP.v20-4006

Subjects:
Primary: 60D05, Primary: 60K37
Secondary: 05C81, 60F17, 60G55

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