Electronic Journal of Probability

Quenched invariance principle for random walks on Delaunay triangulations

Arnaud Rousselle

Full-text: Open access

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.

Article information

Source
Electron. J. Probab., Volume 20 (2015), paper no. 33, 32 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465067139

Digital Object Identifier
doi:10.1214/EJP.v20-4006

Mathematical Reviews number (MathSciNet)
MR3335824

Zentralblatt MATH identifier
1321.60066

Subjects
Primary: Primary: 60K37 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 60G55: Point processes 05C81: Random walks on graphs 60F17: Functional limit theorems; invariance principles

Keywords
Random walk in random environment Delaunay triangulation point process quenched invariance principle isoperimetric inequalities

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Rousselle, Arnaud. Quenched invariance principle for random walks on Delaunay triangulations. Electron. J. Probab. 20 (2015), paper no. 33, 32 pp. doi:10.1214/EJP.v20-4006. https://projecteuclid.org/euclid.ejp/1465067139


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