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

Berger, Quentin; Poisat, Julien (2015), On the critical curves of the pinning and copolymer models in correlated Gaussian environment, Electronic Journal of Probability, 20, p. n°71. 10.1214/EJP.v20-3514

Type
Article accepté pour publication ou publié
External document link
http://arxiv.org/abs/1404.5939v1
Date
2015
Journal name
Electronic Journal of Probability
Volume
20
Publisher
Institute of Mathematical Statistics
Pages
n°71
Publication identifier
10.1214/EJP.v20-3514
Metadata
Show full item record
Author(s)
Berger, Quentin cc
Laboratoire de Probabilités et Modèles Aléatoires [LPMA]
Poisat, Julien
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
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.
Subjects / Keywords
Pinning Model; Copolymer Model; Critical Curve; Fractional Moments; CoarseGraining; Correlations

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