Slowdown for Time Inhomogeneous Branching Brownian Motion

被引：33

作者：

Fang, Ming ^{[2
]}

Zeitouni, Ofer ^{[1
,3
]}

机构：

[1] Univ Minnesota, Minneapolis, MN USA

[2] Xiamen Univ, Sch Math Sci Xiamen, Fujian 361005, Peoples R China

[3] Weizmann Inst Sci, IL-76100 Rehovot, Israel

来源：

JOURNAL OF STATISTICAL PHYSICS | 2012年 / 149卷 / 01期

基金：

美国国家科学基金会; 以色列科学基金会;

关键词：

Branching Brownian motion; Polymers on trees; KPP equation; TRAVELING-WAVES;

D O I：

10.1007/s10955-012-0581-z

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider the maximal displacement of one dimensional branching Brownian motion with (macroscopically) time varying profiles. For monotone decreasing variances, we show that the correction from linear displacement is not logarithmic but rather proportional to T (1/3). We conjecture that this is the worse case correction possible.

引用

页码：1 / 9

页数：9

共 15 条

[1] MINIMA IN BRANCHING RANDOM WALKS [J].

Addario-Berry, Louigi ;

Reed, Bruce .

ANNALS OF PROBABILITY, 2009, 37 (03) :1044-1079

[2]

Aidekon E., ANN PROBAB IN PRESS

[3]

[Anonymous], ELECT J PROBAB

[4]

[Anonymous], 1997, J ROYAL STAT SOC SER

[5]

BRAMSON M, 1983, MEM AM MATH SOC, V44

[6] TIGHTNESS FOR A FAMILY OF RECURSION EQUATIONS [J].

Bramson, Maury ;

Zeitouni, Ofer .

ANNALS OF PROBABILITY, 2009, 37 (02) :615-653

[7] MAXIMAL DISPLACEMENT OF BRANCHING BROWNIAN-MOTION [J].

BRAMSON, MD .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1978, 31 (05) :531-581

[8]

Dembo A., 1998, Large Deviation Techniques and Applications

[9] POLYMERS ON DISORDERED TREES, SPIN-GLASSES, AND TRAVELING WAVES [J].

DERRIDA, B ;

SPOHN, H .

JOURNAL OF STATISTICAL PHYSICS, 1988, 51 (5-6) :817-840

[10]

Fang M, 2010, J APPL PROB IN PRESS

← 1 2 →