L. Arnold, V. Gundlach, and L. , Demetrius: Evolutionary formalism for products of positive random matrices

Y. Bakhtin and K. , Khanin: Localization and Perron?Frobenius theory for directed polymers Mosc, Math. J, vol.10, pp.667-686, 2010.

E. Bates, Localization of directed polymers with general reference walk

E. Bates and S. Chatterjee, The endpoint distribution of directed polymers

N. Bingham, C. Goldie, and J. , Teugels: Regular variation. Encyclopedia of Mathematics and its Applications, 1987.
DOI : 10.1017/cbo9780511721434

J. Bertoin, Subordinators: examples and applications. Lectures on probability theory and statistics (Saint- Flour, Lecture Notes in Math, pp.1-91, 1717.
DOI : 10.1007/978-3-540-48115-7_1

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

P. Bougerol and J. Lacroix, Products of random matrices with applications to Schrdinger operators, Progress in Probability and Statistics, 1985.

A. Bovier, Gaussian processes on trees. From spin glasses to branching Brownian motion, Cambridge Studies in Advanced Mathematics, vol.163, p.2017
DOI : 10.1017/9781316675779

E. Brunet and B. , Derrida: Probability distribution of the free energy of a directed polymer in a random medium, Phys. Rev. E, issue.3 6, pp.61-6789, 2000.

E. Brunet and B. , Exactly soluble noisy traveling-wave equation appearing in the problem of directed polymers in a random medium, Physical Review E, vol.588, issue.1, p.16106, 2004.
DOI : 10.1103/PhysRevE.69.060101
URL : https://hal.archives-ouvertes.fr/hal-00005373

E. Buffet and J. Pulé, Directed polymers on trees: a martingale approach, Journal of Physics A: Mathematical and General, vol.26, issue.8, pp.1823-1834, 1993.
DOI : 10.1088/0305-4470/26/8/011

P. Carmona, F. Guerra, Y. Hu, and O. , Strong Disorder for a Certain Class of Directed Polymers in a Random Environment, Journal of Theoretical Probability, vol.147, issue.2, pp.134-151, 2006.
DOI : 10.1007/978-1-4612-5320-4
URL : https://hal.archives-ouvertes.fr/hal-00128530

J. Cohen and C. Newman, The Stability of Large Random Matrices and Their Products, The Annals of Probability, vol.12, issue.2, pp.283-310, 1984.
DOI : 10.1214/aop/1176993291

F. Comets, Directed polymers in random environments, Lecture Notes in Mathematics, vol.2175, 2017.
DOI : 10.1007/978-3-319-50487-2

F. Comets and J. Quastel-;-a, Last Passage Percolation and Traveling Fronts, Journal of Statistical Physics, vol.33, issue.1, pp.419-451, 2013.
DOI : 10.1214/009117904000000865
URL : https://hal.archives-ouvertes.fr/hal-00677712

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

J. Cook and B. , Derrida: Directed polymers in a random medium: 1/d expansion and the n-tree approximation, J. Phys. A: Math. Gen, pp.23-1523, 1990.

A. Cortines, The genealogy of a solvable population model under selection with dynamics related to directed polymers, Bernoulli, vol.22, issue.4, pp.2209-2236, 2016.
DOI : 10.3150/15-BEJ726

B. Derrida and H. , Polymers on disordered trees, spin glasses, and traveling waves, Journal of Statistical Physics, vol.46, issue.5-6, pp.817-840, 1988.
DOI : 10.1051/jphys:0198500460101700

R. Durrett, Probability: theory and examples. Fourth edition, 2010.
DOI : 10.1017/CBO9780511779398

J. Eckmann and C. , The largest Liapunov exponent for random matrices and directed polymers in a random environment, Communications in Mathematical Physics, vol.50, issue.1, pp.147-175, 1989.
DOI : 10.1007/978-1-4684-6257-9

W. Feller, An introduction to probability theory and its applications, 1971.

H. Furstenberg, Noncommuting random products, Transactions of the American Mathematical Society, vol.108, issue.3, pp.377-428, 1963.
DOI : 10.1090/S0002-9947-1963-0163345-0

H. Furstenberg and H. , Products of Random Matrices, The Annals of Mathematical Statistics, vol.31, issue.2, pp.457-469, 1960.
DOI : 10.1214/aoms/1177705909

Y. Guivarc-'h and A. Raugi, Fronti??re de furstenberg, propri??t??s de contraction et th??or??mes de convergence, Zeitschrift f??r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.15, issue.2, pp.187-242, 1985.
DOI : 10.1137/1110002

D. Henley and C. , Huse: Pinning and roughening of domain wall in Ising systems due to random impurities, Phys. Rev. Lett, vol.54, pp.2708-2711, 1985.

H. Hennion, Limit theorems for products of positive random matrices, The Annals of Probability, vol.25, issue.4, pp.1545-1587, 1997.
DOI : 10.1214/aop/1023481103

H. Hennion and L. , Stable Laws and Products of Positive Random Matrices, Journal of Theoretical Probability, vol.6, issue.1, pp.966-981, 2008.
DOI : 10.1007/b87874
URL : https://hal.archives-ouvertes.fr/hal-00360677

J. Imbrie and T. Spencer, Diffusion of directed polymers in a random environment, Journal of Statistical Physics, vol.58, issue.3-4, pp.609-609, 1988.
DOI : 10.1007/BF01019720

J. Jacod, Theoremes Limite Pour Les Processus, Lecture Notes in Mathematics, vol.1117, pp.298-409, 1983.
DOI : 10.1007/BFb0099423

M. Kardar, G. Parisi, and Y. Zhang, Dynamic Scaling of Growing Interfaces, Physical Review Letters, vol.41, issue.9, pp.889-889, 1986.
DOI : 10.1007/BF01020601

M. Kardar and Y. , Scaling of Directed Polymers in Random Media, Physical Review Letters, vol.58, issue.20, pp.2087-2087, 1987.
DOI : 10.1103/RevModPhys.58.765

M. Leadbetter, G. Lindgren, and H. Rootzén, Extremes and related properties of random sequences and processes, 1983.
DOI : 10.1007/978-1-4612-5449-2

C. Newman, The distribution of Lyapunov exponents: Exact results for random matrices, Communications In Mathematical Physics, vol.298, issue.1, pp.121-126, 1986.
DOI : 10.1007/BF01464284

N. O. Connell and M. Yor, Brownian analogues of Burke's theorem, Stochastic Processes and their Applications, vol.96, issue.2, pp.285-304, 2001.
DOI : 10.1016/S0304-4149(01)00119-3

. Ya, Sina¨?Sina¨?: A random walk with a random potential, Teor. Veroyatnost. i Primenen, vol.38, pp.457-460, 1993.

J. M. Steele, Kingman's subadditive ergodic theorem, Ann. Inst. H. Poincaré Probab. Statist, vol.25, pp.93-98, 1989.

T. Seppäläinen, Scaling for a one-dimensional directed polymer with boundary conditions, The Annals of Probability, vol.40, issue.1, pp.19-73, 2012.
DOI : 10.1214/10-AOP617