Euclidean models of first-passage percolation

被引：0
|
作者：
C. Douglas Howard
Charles M. Newman
机构：
[1] Polytechnic University,
[2] 6 Metrotech Center,undefined
[3] Brooklyn,undefined
[4] NY 11201,undefined
[5] USA (e-mail: howard@math.poly.edu),undefined
[6] Courant Institute of Mathematical Sciences,undefined
[7] New York University,undefined
[8] 251 Mercer Street,undefined
[9] New York,undefined
[10] NY 10012,undefined
[11] USA (e-mail: newman@cims.nyu.edu),undefined
来源：
Probability Theory and Related Fields | 1997年 / 108卷
关键词：
Key words and phrases: First-passage percolation; Poisson process; Voronoi tesselation; shape theorem; geodesic; Mathematics Subject Classification (1991): Primary 60K35; 60G55; secondary 82D30.;
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学科分类号：
摘要：
We introduce a new family of first-passage percolation (FPP) models in the context of Poisson-Voronoi tesselations of ℝd. Compared to standard FPP on ℤd, these models have some technical complications but also have the advantage of statistical isotropy. We prove two almost sure results: a shape theorem (where isotropy implies an exact Euclidean ball for the asymptotic shape) and nonexistence of certain doubly infinite geodesics (where isotropy yields a stronger result than in standard FPP).
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页码：153 / 170
页数：17
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