The construction of the d + 1-dimensional gaussian droplet

G. Ben Arous, J. D. Deuschel

Research output: Contribution to journalArticle

Abstract

The aim of this note is to study the asymptotic behavior of a gaussian random field, under the condition that the variables are positive and the total volume under the variables converges to some fixed number v > 0. In the context of Statistical Mechanics, this corresponds to the problem of constructing a droplet on a hard wall with a given volume. We show that, properly rescaled, the profile of a gaussian configuration converges to a smooth hypersurface, which solves a quadratic variational problem. Our main tool is a scaling dependent large deviation principle for random hypersurfaces.

Original languageEnglish (US)
Pages (from-to)467-488
Number of pages22
JournalCommunications in Mathematical Physics
Volume179
Issue number2
StatePublished - 1996

Fingerprint

Droplet
Hypersurface
Converge
Gaussian Random Field
Large Deviation Principle
statistical mechanics
Statistical Mechanics
Variational Problem
Asymptotic Behavior
Scaling
deviation
scaling
Configuration
Dependent
profiles
configurations
Context
Profile

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

The construction of the d + 1-dimensional gaussian droplet. / Ben Arous, G.; Deuschel, J. D.

In: Communications in Mathematical Physics, Vol. 179, No. 2, 1996, p. 467-488.

Research output: Contribution to journalArticle

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