Scaling limits for weakly pinned random walks with two large deviation minimizers

被引：5

作者：

Funaki, Tadahisa ^{[1
]}

Otobe, Tatsushi ^{[2
]}

机构：

[1] Univ Tokyo, Grad Sch Math Sci, Tokyo 1538914, Japan

[2] Railway Tech Res Inst Kokubunji, Tokyo 1858540, Japan

来源：

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN | 2010年 / 62卷 / 03期

关键词：

scaling limit; large deviation; random walks; pinning;

D O I：

10.2969/jmsj/06231005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The scaling limits for d-dimensional random walks perturbed by an attractive force toward the origin are studied under the critical situation that the rate functional of the corresponding large deviation principle admits two minimizers. Our results extend those obtained by [2] from the mean-zero Gaussian to non-Gaussian setting under the absence of the wall.

引用

页码：1005 / 1041

页数：37

共 13 条

[1] [Anonymous], 1976, WILEY SERIES PROBABI
[2] Critical behavior of the massless free field at the depinning transition
Bolthausen, E
Velenik, Y
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2001, 223 (01) : 161 - 203
[3] Concentration under scaling limits for weakly pinned Gaussian random walks
Bolthausen, Erwin
Funaki, Tadahisa
Otobe, Tatsushi
[J]. PROBABILITY THEORY AND RELATED FIELDS, 2009, 143 (3-4) : 441 - 480
[4] Dembo A., 1998, APPL MATH, V38
[5] Large deviations and concentration properties for Δφ interface models
Deuschel, JD
Giacomin, G
Ioffe, D
[J]. PROBABILITY THEORY AND RELATED FIELDS, 2000, 117 (01) : 49 - 111
[6] Ellis Richard S., 1985, GRUNDLEHREN MATH WIS, V271
[7] Feller W., 1991, An Introduction to Probability Theory and Its Applications
[8] Funaki T., 2004, Adv. Stud. Pure Math, V39, P173
[9] FUNAKI T., 2005, Lecture Notes in Math., V1869, P103, DOI [10.1007/114295792, DOI 10.1007/11429579_2]
[10] Funaki T., 2008, RIMS KOKYUROKU BES B, VB6, P97

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