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
收藏
页数:27
相关论文
共 23 条
[1]  
Alves O., 2002, Electron. J. Probab., V7, P1, DOI DOI 10.1214/EJP.V7-115
[2]  
Alves OSM, 2002, ANN APPL PROBAB, V12, P533
[3]  
Beckman E., 2018, ELECTRON J PROBAB, V23
[4]   Exponential concentration for first passage percolation through modified Poincare inequalities [J].
Benaim, Michel ;
Rossignol, Raphael .
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2008, 44 (03) :544-573
[5]  
Benjamini I, 2003, ANN PROBAB, V31, P1970
[6]   LARGE DEVIATIONS OF THE FRONT IN A ONE-DIMENSIONAL MODEL OF X plus Y → 2X [J].
Berard, Jean ;
Ramirez, Alejandro F. .
ANNALS OF PROBABILITY, 2010, 38 (03) :955-1018
[7]  
Boucheron Stephane, 2013, CONCENTRATION INEQUA
[8]  
Can V. H., UNPUB
[9]  
Chatterjee S, 2014, SPRINGER MONOGR MATH, P1, DOI 10.1007/978-3-319-03886-5
[10]   FLUCTUATIONS OF THE FRONT IN A ONE DIMENSIONAL MODEL OF X plus Y → 2X [J].
Comets, Francis ;
Quastel, Jeremy ;
Ramirez, Alejandro F. .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 361 (11) :6165-6189