Equilibrium fluctuations for ∇φ interface model

Giambattista Giacomin; Stefano Olla; Herbert Spohn

doi:10.1214/aop/1015345600

Equilibrium fluctuations for ∇_φ interface model

Giambattista Giacomin, Stefano Olla, Herbert Spohn

TUM Emeriti of Excellence

Research output: Contribution to journal › Article › peer-review

81 Scopus citations

Abstract

We study the large scale space-time fluctuations of an interface which is modeled by a massless scalar field with reversible Langevin dynamics. For a strictly convex interaction potential we prove that on a large space-time scale these fluctuations are governed by an infinite-dimensional Ornstein-Uhlenbeck process. Its effective diffusion type covariance matrix is characterized through a variational formula.

Original language	English
Pages (from-to)	1138-1172
Number of pages	35
Journal	Annals of Probability
Volume	29
Issue number	3
DOIs	https://doi.org/10.1214/aop/1015345600
State	Published - Jul 2001

Keywords

De Giorgi-Nash-Moser and Aronson estimates
Equilibrium fluctuations
Gibbs measures
Homogenization
Interface model
Langevin dynamics
Massless field

Access to Document

10.1214/aop/1015345600

Cite this

@article{698c5d2d11014468b53fb0956e2de172,

title = "Equilibrium fluctuations for ∇φ interface model",

abstract = "We study the large scale space-time fluctuations of an interface which is modeled by a massless scalar field with reversible Langevin dynamics. For a strictly convex interaction potential we prove that on a large space-time scale these fluctuations are governed by an infinite-dimensional Ornstein-Uhlenbeck process. Its effective diffusion type covariance matrix is characterized through a variational formula.",

keywords = "De Giorgi-Nash-Moser and Aronson estimates, Equilibrium fluctuations, Gibbs measures, Homogenization, Interface model, Langevin dynamics, Massless field",

author = "Giambattista Giacomin and Stefano Olla and Herbert Spohn",

year = "2001",

month = jul,

doi = "10.1214/aop/1015345600",

language = "English",

volume = "29",

pages = "1138--1172",

journal = "Annals of Probability",

issn = "0091-1798",

publisher = "Institute of Mathematical Statistics",

number = "3",

}

TY - JOUR

T1 - Equilibrium fluctuations for ∇φ interface model

AU - Giacomin, Giambattista

AU - Olla, Stefano

AU - Spohn, Herbert

PY - 2001/7

Y1 - 2001/7

N2 - We study the large scale space-time fluctuations of an interface which is modeled by a massless scalar field with reversible Langevin dynamics. For a strictly convex interaction potential we prove that on a large space-time scale these fluctuations are governed by an infinite-dimensional Ornstein-Uhlenbeck process. Its effective diffusion type covariance matrix is characterized through a variational formula.

AB - We study the large scale space-time fluctuations of an interface which is modeled by a massless scalar field with reversible Langevin dynamics. For a strictly convex interaction potential we prove that on a large space-time scale these fluctuations are governed by an infinite-dimensional Ornstein-Uhlenbeck process. Its effective diffusion type covariance matrix is characterized through a variational formula.

KW - De Giorgi-Nash-Moser and Aronson estimates

KW - Equilibrium fluctuations

KW - Gibbs measures

KW - Homogenization

KW - Interface model

KW - Langevin dynamics

KW - Massless field

UR - http://www.scopus.com/inward/record.url?scp=0038845422&partnerID=8YFLogxK

U2 - 10.1214/aop/1015345600

DO - 10.1214/aop/1015345600

M3 - Article

AN - SCOPUS:0038845422

SN - 0091-1798

VL - 29

SP - 1138

EP - 1172

JO - Annals of Probability

JF - Annals of Probability

IS - 3

ER -

Equilibrium fluctuations for ∇_φ interface model

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this