# Localization of a polymer interacting with an interface.

Abstract : We study different models of polymers (discrete and continuous) in the neighborhood of an interface between two solvents
(oil-water). These models give rise to a transition between a localized phase and a delocalized phase. We prove
first several convergence results of discrete models towards their associated continuous counterparts. These convergence
hold when the coupling tends to $0$ (for high temperatures) and concerns the free energy and the slope of the critical
curve at the origin. To that aim, we develop a method of coarse graining, introduced by Bolthausen and den Hollander,
which we generalize to the case of a copolymer under the influence of a random pinning potential along the
oil-water interface. We prove also a pathwise result in the case of a copolymer, which is pulled up and away
from the interface. We show in particular that inside the localized phase, the polymer comes back to the interface
only a finite number of times. Finally, we study the case of an hydrophobic homopolymer in the neighborhood of an
oil-water interface, and also under the influence of a random potential when touching the interface. Through a method
consisting of adapting the law of each excursion to its local random environment, we take into account the fact that
the polymer can target the sites in which it comes back to the interface. This allows us to improve in a quantitative way
the lower bound of the quenched critical curve.
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Cited literature [27 references]

https://tel.archives-ouvertes.fr/tel-00068229
Contributor : Nicolas Pétrélis <>
Submitted on : Thursday, May 11, 2006 - 11:29:01 AM
Last modification on : Tuesday, February 5, 2019 - 11:44:10 AM
Long-term archiving on: : Monday, September 17, 2012 - 2:25:24 PM

### Identifiers

• HAL Id : tel-00068229, version 1

### Citation

Nicolas Pétrélis. Localization of a polymer interacting with an interface.. Mathematics [math]. Université de Rouen, 2006. English. ⟨tel-00068229⟩

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