### 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 language | English (US) |
---|---|

Pages (from-to) | 467-488 |

Number of pages | 22 |

Journal | Communications in Mathematical Physics |

Volume | 179 |

Issue number | 2 |

State | Published - 1996 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Communications in Mathematical Physics*,

*179*(2), 467-488.

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

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 179, no. 2, pp. 467-488.

}

TY - JOUR

T1 - The construction of the d + 1-dimensional gaussian droplet

AU - Ben Arous, G.

AU - Deuschel, J. D.

PY - 1996

Y1 - 1996

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0039613680&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039613680&partnerID=8YFLogxK

M3 - Article

VL - 179

SP - 467

EP - 488

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -