The Critical Curve of the Random Pinning and Copolymer Models at Weak Coupling

Quentin Berger (1) , Francesco Caravenna (2) , Julien Poisat (3) , Rongfeng Sun , Nikos Zygouras

1 Phys-ENS - Laboratoire de Physique de l'ENS Lyon
2 Dipartimento di Matematica e Applicazioni [Milano]
3 Mathematical institute

We study random pinning and copolymer models, when the return distribution of the underlying renewal process has a polynomial tail with finite mean. We compute the asymptotic behavior of the critical curves of the models in the weak coupling regime, showing that it is universal. This proves a conjecture of Bolthausen, den Hollander and Opoku for copolymer models (ref. [8]), which we also extend to pinning models.

Domains: Probability [math.PR]; Mathematical Physics [math-ph]; Mathematical Physics [math-ph]

Quentin Berger, Francesco Caravenna, Julien Poisat, Rongfeng Sun, Nikos Zygouras. The Critical Curve of the Random Pinning and Copolymer Models at Weak Coupling. Communications in Mathematical Physics, 2014, 326 (2), pp.507--530. ⟨10.1007/s00220-013-1849-0⟩. ⟨hal-01068856⟩