Euclidean models of first-passage percolation

被引：65

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 [统计学]; 070103 [概率论与数理统计]; 0714 [统计学];

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

页码：153 / 170

页数：18

共 19 条

[1]

AIZENMAN M, 1996, SCALING LIMIT INCIPI

[2]

BENJAMINI I, 1996, CONFORMAL INVARIANCE

[3]

SOME LIMIT-THEOREMS FOR PERCOLATION PROCESSES WITH NECESSARY AND SUFFICIENT CONDITIONS [J].