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February 2013 On some fundamental aspects of polyominoes on random Voronoi tilings
Leandro P. R. Pimentel
Braz. J. Probab. Stat. 27(1): 54-69 (February 2013). DOI: 10.1214/11-BJPS150

Abstract

Consider a Voronoi tiling of $\mathbb{R} ^{d}$ based on a realization of an inhomogeneous Poisson random set. A Voronoi polyomino is a finite and connected union of Voronoi tiles. In this paper we provide tail bounds for the number of boxes that are intersected by a Voronoi polyomino, and vice-versa. These results will be crucial to analyze self-avoiding paths, greedy polyominoes and first-passage percolation models on Voronoi tilings and on the dual graph, named the Delaunay triangulation [Asymptotics for first-passage times on Delaunay triangulations (2011) Preprint, Greedy Polyominoes and first-passage times on random Voronoi tilings (2012) Preprint].

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Leandro P. R. Pimentel. "On some fundamental aspects of polyominoes on random Voronoi tilings." Braz. J. Probab. Stat. 27 (1) 54 - 69, February 2013. https://doi.org/10.1214/11-BJPS150

Information

Published: February 2013
First available in Project Euclid: 16 October 2012

zbMATH: 1263.60086
MathSciNet: MR2991778
Digital Object Identifier: 10.1214/11-BJPS150

Rights: Copyright © 2013 Brazilian Statistical Association

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Vol.27 • No. 1 • February 2013
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