The construction of the d + 1-dimensional gaussian droplet

G. Ben Arous, J. D. Deuschel

Research output: Contribution to journalArticlepeer-review


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
Issue number2
StatePublished - 1996

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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