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A percolating hard sphere model
Author(s) -
Cotar Codina,
Holroyd Alexander E.,
Revelle David
Publication year - 2009
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.20230
Subject(s) - struct , spheres , invariant (physics) , dimension (graph theory) , homogeneous , poisson distribution , mathematics , poisson point process , point (geometry) , translation (biology) , point process , pure mathematics , statistical physics , combinatorics , physics , geometry , computer science , mathematical physics , statistics , biochemistry , chemistry , astronomy , messenger rna , gene , programming language
Given a homogeneous Poisson point process in ℝ d , Häggström and Meester (Random Struct Algorithms 9 (1996) 295–315) asked whether it is possible to place spheres (of differing radii) centred at the points, in a translation‐invariant way, so that the spheres do not overlap but there is an unbounded component of touching spheres. We prove that the answer is yes in sufficiently high dimension. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2009