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
TypeArticle accepté pour publication ou publié
External document linkhttp://arxiv.org/abs/1404.5939v1
Journal nameElectronic Journal of Probability
Institute of Mathematical Statistics
MetadataShow full item record
Laboratoire de Probabilités et Modèles Aléatoires [LPMA]
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 / KeywordsPinning Model; Copolymer Model; Critical Curve; Fractional Moments; CoarseGraining; Correlations
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Pinning on a defect line: characterization of marginal disorder relevance and sharp asymptotics for the critical point shift Berger, Quentin; Lacoin, Hubert (2018) Article accepté pour publication ou publié