K. S. Alexander, The Effect of Disorder on Polymer Depinning Transitions, Communications in Mathematical Physics, vol.35, issue.1, pp.117-146, 2008.
DOI : 10.1007/s00220-008-0425-5

S. Kenneth, N. Alexander, and . Zygouras, Quenched and annealed critical points in polymer pinning models, Comm. Math. Phys, vol.291, issue.3, pp.659-689, 2009.

S. Kenneth, N. Alexander, and . Zygouras, Equality of critical points for polymer depinning transitions with loop exponent one, Ann. Appl. Probab, vol.20, issue.1, pp.356-366

S. Asmussen, Applied probability and queues, Stochastic Modelling and Applied Probability, p.1978607, 2003.

Q. Berger, Comments on the influence of disorder for pinning model in correlated Gaussian environment, ALEA Lat. Am. J. Probab. Math. Stat, vol.10, issue.2, pp.953-977
URL : https://hal.archives-ouvertes.fr/hal-01426319

Q. Berger, Pinning Model in Random Correlated Environment: Appearance of an Infinite Disorder Regime, Journal of Statistical Physics, vol.27, issue.3, pp.544-570
DOI : 10.1007/s10955-014-0965-3

URL : https://hal.archives-ouvertes.fr/hal-01413009

Q. Berger, F. Caravenna, J. Poisat, R. Sun, and N. Zygouras, The Critical Curves of the Random Pinning and Copolymer Models at Weak Coupling, Communications in Mathematical Physics, vol.14, issue.33, pp.507-530
DOI : 10.1007/s00220-013-1849-0

N. H. Bingham, C. M. Goldie, and J. L. Teugels, Regular variation, volume 27 of Encyclopedia of Mathematics and its Applications, p.898871, 1987.

T. Bodineau and G. Giacomin, On the Localization Transition of Random Copolymers Near Selective Interfaces, Journal of Statistical Physics, vol.117, issue.5-6, pp.801-818, 2004.
DOI : 10.1007/s10955-004-5705-7

URL : https://hal.archives-ouvertes.fr/hal-00103543

T. Bodineau, G. Giacomin, H. Lacoin, and F. L. Toninelli, Copolymers at Selective Interfaces: New Bounds on??the??Phase Diagram, Journal of Statistical Physics, vol.13, issue.4, pp.603-626, 2008.
DOI : 10.1007/s10955-008-9579-y

URL : https://hal.archives-ouvertes.fr/hal-00354956

E. Bolthausen, . Frank, and . Hollander, Localization transition for a polymer near an interface, The Annals of Probability, vol.25, issue.3, pp.1334-1366, 1997.
DOI : 10.1214/aop/1024404516

E. Bolthausen, A. A. Frank-den-hollander, and . Opoku, A copolymer near a selective interface: Variational characterization of the free energy, The Annals of Probability, vol.43, issue.2, pp.875-933
DOI : 10.1214/14-AOP880

F. Caravenna and G. Giacomin, The weak coupling limit of disordered copolymer models, The Annals of Probability, vol.38, issue.6, pp.2322-2378
DOI : 10.1214/10-AOP546

URL : https://hal.archives-ouvertes.fr/hal-00557920

F. Caravenna, G. Giacomin, and M. Gubinelli, Large scale behavior of semiflexible heteropolymers, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.46, issue.1, pp.97-118
DOI : 10.1214/08-AIHP310

URL : https://hal.archives-ouvertes.fr/hal-00485281

F. Caravenna, R. Sun, and N. Zygouras, Polynomial chaos and scaling limits of disordered systems, Journal of the European Mathematical Society, vol.19, issue.1
DOI : 10.4171/JEMS/660

D. Cheliotis, . Frank, and . Hollander, Variational characterization of the critical curve for pinning of random polymers, The Annals of Probability, vol.41, issue.3B, pp.1767-1805
DOI : 10.1214/11-AOP727

I. P. Cornfeld, S. V. Fomin, and Y. G. , Sina? ?. Ergodic theory, of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 1982.

B. Derrida, G. Giacomin, H. Lacoin, and F. L. Toninelli, Fractional Moment Bounds and Disorder Relevance for Pinning Models, Communications in Mathematical Physics, vol.18, issue.3, pp.867-887, 2009.
DOI : 10.1007/s00220-009-0737-0

URL : https://hal.archives-ouvertes.fr/hal-00202700

G. Giacomin, Random polymer models, p.2380992, 2007.
DOI : 10.1142/p504

URL : https://hal.archives-ouvertes.fr/hal-00155080

G. Giacomin, Disorder and critical phenomena through basic probability models Lecture notes from the 40th Probability Summer School held in Saint-Flour, 2010, École d'Été de Probabilités de Saint-Flour. [Saint-Flour Probability Summer School, Lecture Notes in Mathematics, vol.2025, p.2816225, 2011.

G. Giacomin, H. Lacoin, and F. L. Toninelli, Disorder relevance at marginality and critical point shift, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.47, issue.1, pp.148-175
DOI : 10.1214/10-AIHP366

URL : https://hal.archives-ouvertes.fr/hal-00413563

G. Giacomin, H. Lacoin, and F. Toninelli, Marginal relevance of disorder for pinning models, Communications on Pure and Applied Mathematics, vol.14, issue.20, pp.233-265
DOI : 10.1002/cpa.20301

URL : https://hal.archives-ouvertes.fr/hal-00338985

G. Giacomin and F. L. Toninelli, Smoothing Effect of Quenched Disorder on Polymer Depinning Transitions, Communications in Mathematical Physics, vol.46, issue.1, pp.1-16, 2006.
DOI : 10.1007/s00220-006-0008-2

URL : https://hal.archives-ouvertes.fr/hal-00015489

G. Giacomin and F. L. Toninelli, The localized phase of disordered copolymers with adsorption, ALEA Lat. Am. J. Probab. Math. Stat, vol.1, pp.149-180, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00086236

U. Grenander and G. Szegö, Toeplitz forms and their applications. California Monographs in Mathematical Sciences, p.94840, 1958.
DOI : 10.1063/1.3062237

J. M. Hammersley, Generalization of the fundamental theorem on sub-additive functions, Proc. Cambridge Philos. Soc, pp.235-238, 1962.

A. B. Harris, Effect of random defects on the critical behaviour of Ising models, Journal of Physics C: Solid State Physics, vol.7, issue.9, pp.1671-1692, 1974.
DOI : 10.1088/0022-3719/7/9/009

H. Lacoin, The Martingale approach to disorder irrelevance for pinning models, Electronic Communications in Probability, vol.15, issue.0, pp.418-427
DOI : 10.1214/ECP.v15-1572

C. Monthus, On the localization of random heteropolymers at the interface between two selective solvents, The European Physical Journal B, vol.13, issue.1, pp.111-130, 2000.
DOI : 10.1007/s100510050016

URL : https://hal.archives-ouvertes.fr/hal-00003893

J. Poisat, Ruelle-Perron-Frobenius operator approach to the annealed pinning model with Gaussian long-range correlated disorder, Markov Process. Related Fields, vol.19, issue.3, pp.577-606
URL : https://hal.archives-ouvertes.fr/hal-00755110

G. Pólya, Remarks on characteristic functions, Proceedings of the Berkeley Symposium on Mathematical Statistics and Probability, pp.115-123, 1945.

F. L. Toninelli, A Replica-Coupling Approach to Disordered Pinning Models, Communications in Mathematical Physics, vol.163, issue.1, pp.389-401, 2008.
DOI : 10.1007/s00220-008-0469-6

F. L. Toninelli, Disordered pinning models and copolymers: Beyond annealed bounds, The Annals of Applied Probability, vol.18, issue.4, pp.1569-1587, 2008.
DOI : 10.1214/07-AAP496

F. L. Toninelli, Coarse graining, fractional moments and the critical slope of random copolymers, Electronic Journal of Probability, vol.14, issue.0, pp.531-547, 2009.
DOI : 10.1214/EJP.v14-612

. Acknowledgments, QB acknowledges support by a travel grant from the Simons Foundation JP acknowledges the support of ERC Advanced Grant 267356 VARIS and ANR project MEMEMO2 Part of this work was carried out during the YEP conference and the following workshop on Random Polymers at EURANDOM in, pp.10-0125, 2013.

@. Submit, E. @bullet-choose, and E. , ECP over for-profit journals 1 OJS: Open Journal Systems http: Lots of Copies Keep Stuff Safe http, sfu.ca/ojs/ 2 IMS: Institute of Mathematical Statistics