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On the critical curves of the pinning and copolymer models in correlated Gaussian environment

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Date
2015
Link to item file
http://arxiv.org/abs/1404.5939v1
Dewey
Analyse
Sujet
Pinning Model; Copolymer Model; Critical Curve; Fractional Moments; CoarseGraining; Correlations
Journal issue
Electronic Journal of Probability
Volume
20
Publication date
2015
Article pages
n°71
Publisher
Institute of Mathematical Statistics
DOI
http://dx.doi.org/10.1214/EJP.v20-3514
URI
https://basepub.dauphine.fr/handle/123456789/15680
Collections
  • CEREMADE : Publications
Metadata
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Author
Berger, Quentin
102 Laboratoire de Probabilités et Modèles Aléatoires [LPMA]
Poisat, Julien
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Article accepté pour publication ou publié
Abstract (EN)
We investigate the disordered copolymer and pinning models, in the case of a correlated Gaussian environment with correlations, and when the return distribution of the underlying renewal process has a polynomial tail. As far as the copolymer model is concerned, we prove disorder relevance both in terms of critical points and critical exponents, in the case of non-negative correlations. When some of the correlations are negative, even the annealed model becomes non-trivial. Moreover, when the return distribution has a finite mean, we are able to compute the weak coupling limit of the critical curves for both models, with no restriction on the correlations other than summability. This generalizes the result of Berger,Caravennale, Poisat, Sun and Zygouras to the correlated case. Interestingly, in the copolymer model, the weak coupling limit of the critical curve turns out to be the maximum of two quantities: one generalizing the limit found in the IID case, the other one generalizing the so-called Monthus bound.

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