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Percolation in Voronoi tilings
Author(s) -
Balister P.,
Bollobás B.,
Quas A.
Publication year - 2005
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20043
Subject(s) - voronoi diagram , percolation (cognitive psychology) , realization (probability) , combinatorics , mathematics , poisson distribution , phase transition , discrete mathematics , mathematical physics , statistical physics , physics , geometry , condensed matter physics , statistics , neuroscience , biology
We consider a percolation process on a random tiling of ℝ d into Voronoi cells based on points of a realization of a Poisson process. We prove the existence of a phase transition as the proportion p of open cells is varied and provide estimates for the critical probability p c . Specifically, we prove that for large d , 2 − d (9 d log d ) −1 ≤ p c ( d ) ≤ C 2 − d $\sqrt{d}$ log d . © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2005
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