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
收藏
页码：1486 / 1499
页数：14
相关论文
共 50 条
  • [31] Large time asymptotics for the parabolic Anderson model driven by space and time correlated noise
    Huang, Jingyu
    Le, Khoa
    Nualart, David
    STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS, 2017, 5 (04): : 614 - 651
  • [32] Soliton solutions for a generalized (1+1)-dimensional equation
    Wang, Dan
    Zhang, Jin-Yu
    Li, Chun-Hui
    Wang, Xiao-Li
    2ND INTERNATIONAL CONFERENCE ON APPLIED MATHEMATICS, MODELLING, AND INTELLIGENT COMPUTING (CAMMIC 2022), 2022, 12259
  • [33] The classifying space of the 1+1 dimensional cobordism category
    Tillmann, U
    JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1996, 479 : 67 - 75
  • [34] Gauging Yang-Mills symmetries in (1+1)-dimensional space-time
    Almukahhal, RQ
    Hübsch, T
    INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 2001, 16 (29): : 4713 - 4768
  • [35] A note on the Duffin-Kemmer-Petiau equation in (1+1) space-time dimensions
    Lunardi, Jose T.
    JOURNAL OF MATHEMATICAL PHYSICS, 2017, 58 (12)
  • [36] Various optical solutions to the (1+1)-Telegraph equation with space-time conformable derivatives
    Gasmi, Boubeker
    Kessi, Arezki
    Jarad, Fahd
    Hammouch, Zakia
    INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 2021, 12 : 767 - 780
  • [37] Longtime asymptotics of the two-dimensional parabolic Anderson model with white-noise potential
    Koenig, Wolfgang
    Perkowski, Nicolas
    van Zuijlen, Willem
    ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2022, 58 (03): : 1351 - 1384
  • [38] Fission and fusion of solitons for the (1+1)-dimensional Kupershmidt equation
    Ying, JP
    COMMUNICATIONS IN THEORETICAL PHYSICS, 2001, 35 (04) : 405 - 408
  • [39] Qualitative analysis and optical solitons for the (1+1)-dimensional Biswas-Milovic equation with parabolic law and nonlocal nonlinearity
    Li, Zhao
    Hussain, Ejaz
    RESULTS IN PHYSICS, 2024, 56
  • [40] Two-Dimensional Gross-Pitaevskii Equation With Space-Time White Noise
    de Bouard, Anne
    Debussche, Arnaud
    Fukuizumi, Reika
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2023, 2023 (12) : 10556 - 10614
12345