Sublinear variance in first-passage percolation for general distributions

被引：17

作者：

Damron, Michael ^{[1
]}

Hanson, Jack ^{[2
]}

Sosoe, Philippe ^{[1
]}

机构：

[1] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

[2] Princeton Univ, Dept Phys, Princeton, NJ 08544 USA

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2015年 / 163卷 / 1-2期

基金：

美国国家科学基金会; 加拿大自然科学与工程研究理事会;

关键词：

Primary; 60K35; Secondary; 60E15;

D O I：

10.1007/s00440-014-0591-7

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 prove that the variance of the passage time from the origin to a point in first-passage percolation on is sublinear in the distance to when , obeying the bound , under minimal assumptions on the edge-weight distribution. The proof applies equally to absolutely continuous, discrete and singular continuous distributions and mixtures thereof, and requires only moments. The main result extends work of Benjamini-Kalai-Schramm (Ann Prob 31, 2003) and Benaim-Rossignol (Ann Inst Henri Poincar, Prob Stat 3, 2008).

引用

页码：223 / 258

页数：36

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