G. Benarous et Jd. Deuschel, THE CONSTRUCTION OF THE D-DIMENSIONAL GAUSSIAN DROPLET(1), Communications in Mathematical Physics, 179(2), 1996, pp. 467-488
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 configurat
ion converges to a smooth hypersurface, which solves a quadratic varia
tional problem. Our main tool is a scaling dependent large deviation p
rinciple for random hypersurfaces.