We consider the lattice version of the free field in two dimensions
(also called harmonic crystal). The main aim of the paper is to discuss
quantitatively the entropic repulsion of the random surface in the presence of
a hard wall. The basic ingredient of the proof is the analysis of the maximum
of the field which requires a multiscale analysis reducing the problem
essentially to a problem on a field with a tree structure.
Publié le : 2001-10-14
Classification:
Free field,
effective interface models,
entropic repulsion,
large deviations,
extrema of Gaussian fields,
multiscale decomposition,
60K35,
60G15,
82B41
@article{1015345767,
author = {Bolthausen, Erwin and Deuschel, Jean-Dominique and Giacomin, Giambattista},
title = {Entropic Repulsion and the Maximum of the two-dimensional
harmonic},
journal = {Ann. Probab.},
volume = {29},
number = {1},
year = {2001},
pages = { 1670-1692},
language = {en},
url = {http://dml.mathdoc.fr/item/1015345767}
}
Bolthausen, Erwin; Deuschel, Jean-Dominique; Giacomin, Giambattista. Entropic Repulsion and the Maximum of the two-dimensional
harmonic. Ann. Probab., Tome 29 (2001) no. 1, pp. 1670-1692. http://gdmltest.u-ga.fr/item/1015345767/