Université Paris 6
Pierre et Marie Curie | Université Paris 7
Denis Diderot | |

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60K35 Interacting random processes; statistical mechanics type models; percolation theory, See also {82B43, 82C43}
- 82B24 Interface problems
- 60G15 Gaussian processes

**Résumé:** We consider two independent lattice harmonic crystals in dimension larger
than two
constrained to live in the upper half plane and
to lie one above the other in a large
region. We identify the leading order
asymptotics of this model, both from the point
of view of probability estimates and of
pathwise behavior: this gives a rather complete
picture of the phenomenon
via a detailed analysis of the
underlying entropy--energy competition.
>From the technical viewpoint,
with respect to earlier work on sharp constants for
harmonic entropic repulsion, this model
is lacking certain monotonicity properties
and the main tool that allows to overcome this
difficulty
is the comparison with suitable rough substrate
models.

**Mots Clés:** *Harmonic Crystal ; Entropic Repulsion ; Multi--interface phenomena ;
Gaussian fields ; Extrema of Random Fields ; Large Deviations ;
Random Walks*

**Date:** 2002-12-18

**Prépublication numéro:** *PMA-780*

**Pdf file : **PMA-780.pdf