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]
- 82B41 Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41]
- 60K37 Processes in random environments

**Résumé:** In this note we consider the (de)localization transition for random
directed (1+1)-dimensional copolymers in the proximity of an
interface separating selective solvents.
We derive a rigorous lower bound on the free energy.
This yields a substantial improvement on the bounds
from below on the critical line that were known so far.
Our result implies that the critical curve does not lie below
the critical curve conjectured by Monthus [Eur. Phys. Journal B 13
(2000), 111-130]
on the base of a renormalization group analysis. We discuss
this result in the light of the (rigorous and non rigorous) approaches
present in the literature and, by making an analogy with a particular
asymptotics of a disordered wetting model, we propose a simplified
framework
in which the question of identifying the critical curve, as well as
understanding the nature of the transition, may be approached.

**Mots Clés:** *Copolymers ; Localization Transition ; Large Deviations ;
Wetting Models*

**Date:** 2004-04-05

**Prépublication numéro:** *PMA-902*