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

Univ-Paris Diderot Sorbonne Paris-Cité
Cergy Pontoise University
École Polytechnique

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

83 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

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10.1214/aop/1015345600

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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",

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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 - https://www.scopus.com/pages/publications/0038845422

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JO - Annals of Probability

JF - Annals of Probability

IS - 3

ER -

Equilibrium fluctuations for ∇_φ interface model

Abstract

Keywords

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