First passage time of the frog model has a sublinear variance

被引：5

作者：

Can, Van Hao ^{[1
,2
]}

Nakajima, Shuta ^{[3
]}

机构：

[1] Kyoto Univ, Res Inst Math Sci, Kyoto 6068502, Japan

[2] Vietnam Acad Sci & Technol, Inst Math, 18 Hoang Quoc Viet, Hanoi 10307, Vietnam

[3] Nagoya Univ, Grad Sch Math, Chikusa Ku, Furocho, Nagoya, Aichi 4640814, Japan

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2019年 / 24卷

基金：

日本学术振兴会;

关键词：

frog model; first passage time; sublinear variance; ONE-DIMENSIONAL MODEL; X PLUS Y; TRANSIENCE; RECURRENCE; PERCOLATION; POINCARE;

D O I：

10.1214/19-EJP334

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：

In this paper, we show that the first passage time in the frog model on Z(d) with d >= 2 has a sublinear variance. This implies that the central limit theorem does not hold at least with the standard diffusive scaling. The proof is based on the method introduced in [4, 11] combined with a control of the maximal weight of paths in a locally dependent site-percolation. We also apply this method to get the linearity of the lengths of optimal paths.

引用

页数：27