T. Alberts, K. Khanin, and J. Quastel, The intermediate disorder regime for directed polymers in dimension $1+1$, The Annals of Probability, vol.42, issue.3, pp.42-1212, 2014.
DOI : 10.1214/13-AOP858

K. S. Alexander and G. Yildirim, Directed polymers in a random environment with a defect line, Electronic Journal of Probability, vol.20, issue.0, 2015.
DOI : 10.1214/EJP.v20-3379

K. S. Alexander and N. Zygouras, Subgaussian concentration and rates of convergence in directed polymers, Electronic Journal of Probability, vol.18, issue.0, 2013.
DOI : 10.1214/EJP.v18-2005

Q. Berger and H. Lacoin, PINNING ON A DEFECT LINE: CHARACTERIZATION OF MARGINAL DISORDER RELEVANCE AND SHARP ASYMPTOTICS FOR THE CRITICAL POINT SHIFT, Journal of the Institute of Mathematics of Jussieu, vol.2025
DOI : 10.1063/1.4895760
URL : https://hal.archives-ouvertes.fr/hal-01141691

N. H. Bingham, C. M. Goldie, and J. L. Teugels, Regular Variations, 1987.
DOI : 10.1017/CBO9780511721434

E. Bolthausen, A note on the diffusion of directed polymers in a random environment, Communications in Mathematical Physics, vol.52, issue.4, pp.529-534, 1989.
DOI : 10.1007/BF01218584

F. Caravenna, R. Sun, and N. Zygouras, Polynomial chaos and scaling limits of disordered systems, to appear in J. Eur, Math. Soc. (JEMS)

F. Caravenna, R. Sun, and N. Zygouras, Universality in marginally relevant disordered systems

F. Caravenna, F. Toninelli, and N. Torri, Universality for the pinning model in the weak coupling regime, preprint

P. Carmona and Y. Hu, On the partition function of a directed polymer in a random Gaussian environment, Probab. Theor. Relat. Fields, vol.124, pp.3-431, 2002.

P. Carmona and Y. Hu, Strong disorder implies strong localization for directed polymers in a random environment, pp.217-229, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00018048

F. Comets, Weak disorder for low dimensional polymers: The model of stable laws, Markov Proc. Rel. Fields 13, pp.681-696, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00204644

F. Comets and V. Vargas, Majorizing multiplicative cascades for directed polymers in random media, pp.267-277, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00012577

F. Comets, T. Shiga, and N. Yoshida, Directed polymers in a random environment: path localization and strong disorder, Bernoulli, vol.9, issue.4, pp.705-723, 2003.
DOI : 10.3150/bj/1066223275
URL : https://hal.archives-ouvertes.fr/hal-00103820

F. Comets, T. Shiga, and N. Yoshida, Probabilistic analysis of directed polymers in a random environment: a review, Adv. Stud. Pure Math, vol.39, pp.115-142, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00104909

F. Comets and N. Yoshida, Directed polymers in random environment are diffusive at weak disorder, The Annals of Probability, vol.34, issue.5, pp.5-1746, 2006.
DOI : 10.1214/009117905000000828
URL : https://hal.archives-ouvertes.fr/hal-00003250

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, 2007.
DOI : 10.1142/p504
URL : https://hal.archives-ouvertes.fr/hal-00155080

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, 2011.
DOI : 10.1214/10-AIHP366
URL : https://hal.archives-ouvertes.fr/hal-00413563

D. A. Huse and C. L. Henley, Pinning and Roughening of Domain Walls in Ising Systems Due to Random Impurities, Physical Review Letters, vol.54, issue.25, pp.2708-2711, 1985.
DOI : 10.1103/PhysRevLett.54.2708

J. Z. Imbrie and T. Spencer, Diffusion of directed polymers in a random environment, Journal of Statistical Physics, vol.58, issue.3-4, pp.608-626, 1988.
DOI : 10.1007/BF01019720

H. Lacoin, New Bounds for the Free Energy of Directed Polymers in Dimension 1??+??1 and 1??+??2, Communications in Mathematical Physics, vol.134, issue.3/4, pp.471-503, 2010.
DOI : 10.1007/s00220-009-0957-3
URL : https://hal.archives-ouvertes.fr/hal-00361863

M. Ledoux, The concentration of measure phenomenon, 2005.
DOI : 10.1090/surv/089

M. Nakashima, A remark on the bound for the free energy of directed polymers in random environment in 1+2 dimension, Journal of Mathematical Physics, vol.55, issue.9, p.93304, 2014.
DOI : 10.1063/1.4895760

M. Miura, Y. Tawarab, and K. Tsuchida, Strong and Weak Disorder for L??vy Directed Polymers in Random Environment, Stochastic Analysis and Applications, vol.13, issue.5, pp.5-1000, 2008.
DOI : 10.1007/s00440-005-0470-3

T. Sasamoto and H. Spohn, Exact height distributions for the KPZ equation with narrow wedge initial condition, Nuclear Physics B, vol.834, issue.3, pp.523-542, 2010.
DOI : 10.1016/j.nuclphysb.2010.03.026

T. Sasamoto and H. Spohn, One-Dimensional Kardar-Parisi-Zhang Equation: An Exact Solution and its Universality, Physical Review Letters, vol.104, issue.23, p.230602, 2010.
DOI : 10.1103/PhysRevLett.104.230602

A. Yilmaz and O. Zeitouni, Differing Averaged and Quenched Large Deviations for Random Walks in Random Environments in Dimensions Two and Three, Communications in Mathematical Physics, vol.26, issue.4, pp.243-271, 2010.
DOI : 10.1007/s00220-010-1119-3

F. Watbled, Sharp asymptotics for the free energy of 1+1 dimensional directed polymers in an infinitely divisible environment, Electronic Communications in Probability, vol.17, issue.0, pp.17-2012
DOI : 10.1214/ECP.v17-2221
URL : https://hal.archives-ouvertes.fr/hal-00723044