On Some fundamental aspects of Polyominoes on Random Voronoi Tilings

Details On Some fundamental aspects of Polyominoes on Random Voronoi Tilings On Some fundamental aspects of Polyominoes on Random Voronoi Tilings

2010-09-20

arxiv.org/abs/1009.3898v2

Mathematics

Probability

Scientific paper

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.

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