Precise intermittency for the parabolic Anderson equation with an (1+1)-dimensional time-space white noise

被引：32

作者：

Chen, Xia ^{[1
]}

机构：

[1] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2015年 / 51卷 / 04期

关键词：

Intermittency; White noise; Brownian motion; Parabolic Anderson model; Feynman-Kac's representation; Ground state energy; STOCHASTIC HEAT-EQUATION;

D O I：

10.1214/15-AIHP673

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：

The moment Lyapunov exponent is computed for the solution of the parabolic Anderson equation with an (1 + 1)-dimensional time-space white noise. Our main result positively confirms an open problem posted in (Ann. Probab. (2015) to appear) and originated from the observations made in the physical literature (J. Statist. Phys. 78 (1995) 1377-1401) and (Nuclear Physics B 290 (1987) 582-602). By a link through the Feynman-Kac's formula, our theorem leads to the evaluation of the ground state energy for the n-body problem with Dirac pair interaction.

引用

页码：1486 / 1499

页数：14

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