The Edwards-Wilkinson Limit of the Random Heat Equation in Dimensions Three and Higher

被引：33

作者：

Gu, Yu ^{[1
]}

Ryzhik, Lenya ^{[2
]}

Zeitouni, Ofer ^{[3
]}

机构：

[1] Carnegie Mellon Univ, Pittsburgh, PA 15213 USA

[2] Stanford Univ, Stanford, CA 94305 USA

[3] Weizmann Inst Sci, Rehovot, Israel

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2018年 / 363卷 / 02期

基金：

以色列科学基金会;

关键词：

DIRECTED POLYMERS; INTEGRAL-REPRESENTATION; THEOREM; DIFFUSION; TIME;

D O I：

10.1007/s00220-018-3202-0

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider the heat equation with a multiplicative Gaussian potential in dimensions d >= 3. We show that the renormalized solution converges to the solution of a deterministic diffusion equation with an effective diffusivity. We also prove that the renormalized large scale random fluctuations are described by the Edwards-Wilkinson model, that is, the stochastic heat equation (SHE) with additive white noise, with an effective variance.

引用

页码：351 / 388

页数：38

共 43 条

[1] The Edwards–Wilkinson Limit of the Random Heat Equation in Dimensions Three and Higher
Yu Gu
Lenya Ryzhik
Ofer Zeitouni
Communications in Mathematical Physics, 2018, 363 : 351 - 388
[2] Smoothening of a random surface as it results from the Edwards-Wilkinson kinetic equation
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CZECHOSLOVAK JOURNAL OF PHYSICS, 1999, 49 (07) : 1017 - 1025
[3] Depinning transition of the quenched Edwards-Wilkinson equation
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[4] Scaling of time-fractional Edwards-Wilkinson equation
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[5] Edwards-Wilkinson equation from lattice transition rules
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[6] In search of smooth sandpiles: The Edwards-Wilkinson equation with flow
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[7] The Edwards-Wilkinson equation with drift and Neumann boundary conditions
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[8] Edwards-Wilkinson depinning transition in random Coulomb potential background
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[9] Revisiting random deposition with surface relaxation: approaches from growth rules to the Edwards-Wilkinson equation
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JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2014,
[10] Effective Edwards-Wilkinson equation for single-file diffusion
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PHYSICAL REVIEW E, 2010, 81 (06):

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