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]
- 60F10 Large deviations
- 82B41 Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41]

**Résumé:** We study the path properties for the delta-pinning wetting model in
(1+1)-dimension.
In other terms, we consider a random walk model with fairly general
continuous
increments conditioned to stay in the upper half plane and with a
delta-measure reward
for touching zero, that is the boundary of the forbidden region.
It is well known that such a model displays a
localization/delocalization transition,
according to the size of the reward. Our focus is on getting a precise
pathwise description of the system, in both the delocalized phase, that
includes
the critical case, and in the localized one.
From this we extract the (Brownian) scaling limits of the model.

**Mots Clés:** *Wetting Transition ; Critical Wetting ; delta-Pinning Model ; Fluctuations of
Random Walks ; Brownian scaling*

**Date:** 2004-04-05

**Prépublication numéro:** *PMA-901*