Euclidean models of first-passage percolation

被引：60
|
作者：
Howard, CD [1 ]
Newman, CM [1 ]
机构：
[1] NYU,COURANT INST MATH SCI,NEW YORK,NY 10012
来源：
PROBABILITY THEORY AND RELATED FIELDS | 1997年 / 108卷 / 02期
关键词：
first-passage percolation; Poisson process; Voronoi tesselation; shape theorem; geodesic;
D O I：
10.1007/s004400050105
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We introduce a new family of first-passage percolation (FPP) models in the context of Poisson-Voronoi tesselations of R-d. Compared to standard FPP on Z(d), 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).
引用
收藏
页码：153 / 170
页数：18
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