THE STOCHASTIC HEAT-EQUATION - FEYNMAN-KAC FORMULA AND INTERMITTENCE

被引：164

作者：

BERTINI, L

CANCRINI, N

机构：

[1] UNIV ROMA TOR VERGATA,DIPARTIMENTO MATEMAT,I-00133 ROME,ITALY

[2] UNIV ROMA LA SAPIENZA,DIPARTIMENTO FIS,I-00185 ROME,ITALY

来源：

JOURNAL OF STATISTICAL PHYSICS | 1995年 / 78卷 / 5-6期

关键词：

STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS; FEYNMAN-KAC FORMULA; RANDOM MEDIA; MOMENT LYAPUNOV EXPONENTS; INTERMITTENCE; LOCAL TIMES;

D O I：

10.1007/BF02180136

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We study, in one space dimension, the heat equation with a random potential that is a white noise in space and time. This equation is a linearized model for the evolution of a scalar field in a space-time-dependent random medium. It has also been related to the distribution of two-dimensional directed polymers in a random environment, to the KPZ model of growing interfaces, and to the Burgers equation with conservative noise. We show how the solution can be expressed via a generalized Feynman-Kac formula. We then investigate the statistical properties: the two-point correlation function is explicitly computed and the intermittence of the solution is proven. This analysis is carried out showing how the statistical moments can be expressed through local times of independent Brownian motions.

引用

页码：1377 / 1401

页数：25

共 17 条

[1]

BAXENDALE PH, 1992, CAMS922 PREPR

[2] THE STOCHASTIC BURGERS-EQUATION [J].

BERTINI, L ;

CANCRINI, N ;

JONALASINIO, G .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1994, 165 (02) :211-232

[3]

BERTINI L, 1993, IN PRESS AUG P NATO

[4]

BOGACHEV LV, 1991, 116 I MATH RUHR U PR

[5]

CANCRINI N, 1993, THESIS U ROMA SAPIEN

[6]

DAPRATO G, 1993, 27 SCUOL NORM SUP PR

[7]

Gikhman I.I., 1972, STOCHASTIC DIFFERENT

[8] THE BURGERS-EQUATION WITH A NOISY FORCE AND THE STOCHASTIC HEAT-EQUATION [J].

HOLDEN, H ;

LINDSTROM, T ;

OKSENDAL, B ;

UBOE, J ;

ZHANG, TS .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1994, 19 (1-2) :119-141

[9] DYNAMIC SCALING OF GROWING INTERFACES [J].

KARDAR, M ;

PARISI, G ;

ZHANG, YC .

PHYSICAL REVIEW LETTERS, 1986, 56 (09) :889-892

[10] SCALING OF DIRECTED POLYMERS IN RANDOM-MEDIA [J].

KARDAR, M ;

ZHANG, YC .

PHYSICAL REVIEW LETTERS, 1987, 58 (20) :2087-2090

← 1 2 →