On Some fundamental aspects of Polyominoes on Random Voronoi Tilings
Probability
2011-08-15 v2 Mathematical Physics
math.MP
Abstract
Consider a Voronoi tiling of the Euclidean space based on a realization of a 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.
Keywords
Cite
@article{arxiv.1009.3898,
title = {On Some fundamental aspects of Polyominoes on Random Voronoi Tilings},
author = {Leandro P. R. Pimentel},
journal= {arXiv preprint arXiv:1009.3898},
year = {2011}
}