Brazilian Journal of Probability and Statistics

On some fundamental aspects of polyominoes on random Voronoi tilings

Leandro P. R. Pimentel

Full-text: Open access

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].

Article information

Source
Braz. J. Probab. Stat., Volume 27, Number 1 (2013), 54-69.

Dates
First available in Project Euclid: 16 October 2012

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1350394629

Digital Object Identifier
doi:10.1214/11-BJPS150

Mathematical Reviews number (MathSciNet)
MR2991778

Zentralblatt MATH identifier
1263.60086

Keywords
Voronoi tilings Delaunay triangulations polyominoes self-avoiding paths

Citation

Pimentel, Leandro P. R. On some fundamental aspects of polyominoes on random Voronoi tilings. Braz. J. Probab. Stat. 27 (2013), no. 1, 54--69. doi:10.1214/11-BJPS150. https://projecteuclid.org/euclid.bjps/1350394629


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