S. Albeverio and X. Zhou, A martingale approach to directed polymers in a random environment, Journal of Theoretical Probability, vol.60, issue.1, pp.171-189, 1996.
DOI : 10.1007/BF02213739

F. Anselmet, R. A. Antonia, Y. Gagne, and E. J. Hopfinger, High-order velocity structure functions in turbulent shear flows, Journal of Fluid Mechanics, vol.17, issue.-1, pp.140-63, 1984.
DOI : 10.1063/1.863407

E. Bacry, J. Delour, and J. Muzy, Modelling financial time series using multifractal random walks, Physica A: Statistical Mechanics and its Applications, vol.299, issue.1-2, pp.299-84, 2001.
DOI : 10.1016/S0378-4371(01)00284-9

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.6.8626

E. Bacry and J. Muzy, Log-Infinitely Divisible Multifractal Processes, Communications in Mathematical Physics, vol.236, issue.3, pp.449-475, 2003.
DOI : 10.1007/s00220-003-0827-3

URL : https://hal.archives-ouvertes.fr/hal-00012441

E. Bacry, A. Kozhemyak, and J. Muzy, Continuous cascade models for asset returns, Journal of Economic Dynamics and Control, vol.32, issue.1
DOI : 10.1016/j.jedc.2007.01.024

URL : https://hal.archives-ouvertes.fr/hal-00604449

M. Birkner, A Condition for Weak Disorder for Directed Polymers in Random Environment, Electronic Communications in Probability, vol.9, issue.0, pp.22-25, 2004.
DOI : 10.1214/ECP.v9-1104

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

E. Brunet and B. Derrida, Probability distribution of the free energy of a directed polymer in a random medium, Physical Review E, vol.61, issue.6, pp.61-6789, 2000.
DOI : 10.1103/PhysRevE.61.6789

P. Carmona and Y. Hu, On the partition function of a directed polymer in a random environment, Probability Theory and Related Fields, vol.124, issue.3, pp.431-457, 2002.
DOI : 10.1007/s004400200213

P. Carmona and Y. Hu, Fluctuation exponents and large deviations for directed polymers in a random environment, Stochastic Processes and their Applications, vol.112, issue.2, pp.285-308, 2004.
DOI : 10.1016/j.spa.2004.03.006

URL : https://hal.archives-ouvertes.fr/hal-00102255

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 and N. Yoshida, Brownian Directed Polymers in Random Environment, Communications in Mathematical Physics, vol.34, issue.2, pp.257-287, 2004.
DOI : 10.1007/s00220-004-1203-7

URL : https://hal.archives-ouvertes.fr/hal-00101805

F. Comets, T. Shiga, and N. Yoshida, Probabilistic analysis of directed polymers in random environment Stochastic analysis on scale interacting systems, Advanced Studies in Pure Mathematics Math. Soc. Japan, vol.39, pp.115-142, 2004.

F. Comets and N. Yoshida, Some new results on Brownian directed polymers in random environment, RIMS Kokyuroku, pp.1386-50, 2004.

F. Comets and N. Yoshida, Directed polymers in random environment are diffusive at weak disorder, arXiv:math

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

D. J. Daley and D. Vere-jones, An introduction to the theory of point processes, 1988.

J. Duchon and R. Robert, Inertial energy dissipation for weak solutions of incompressible Euler and Navier-Stokes equations, Nonlinearity, vol.13, issue.1, pp.249-255, 2000.
DOI : 10.1088/0951-7715/13/1/312

J. Duchon and R. Robert, Champs aléatoires intermittents. Partie I: champs à accroissements symétriques (French) [Intermittent random fields. I. Fields with symmetric increments, pp.265-268, 2005.

J. Duchon and R. Robert, Champs aléatoires intermittents. Partie II: champs à accroissements dissymétriques (French) [Intermittent random fields. II. Fields with asymmetric increments, pp.329-331, 2005.

R. Durrett, Oriented Percolation in Two Dimensions, The Annals of Probability, vol.12, issue.4, pp.999-1040, 1984.
DOI : 10.1214/aop/1176993140

R. Durrett and T. Liggett, Fixed points of the smoothing transformation, Zeitschrift f??r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.39, issue.3, pp.275-301, 1983.
DOI : 10.1007/BF00532962

J. Franchi, Chaos multiplicatif: un traitement simple et complet de la fonction de partition, Séminaire de Probabilités XXIX, Lecture notes in Math, pp.194-201, 2000.

P. Hall and C. C. Heyde, Martingale limit theory and its Application, Probabilty and Mathematical Statistics, 1980.

T. Halpin-healy and N. Pang, Discerning differences among anomalously wandering directed polymers, Physical Review E, vol.47, issue.2, pp.784-786, 1993.

T. Halpin-healy and Y. C. Zhang, Kinetic roughening phenomena, stochastic growth, directed polymers and all that. Aspects of multidisciplinary statistical mechanics, Physics Reports, vol.254, issue.4-6, pp.215-414, 1995.
DOI : 10.1016/0370-1573(94)00087-J

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.609-626, 1988.
DOI : 10.1007/BF01019720

K. Johansson, Shape Fluctuations and Random Matrices, Communications in Mathematical Physics, vol.209, issue.2, pp.437-476, 2000.
DOI : 10.1007/s002200050027

J. Kahane, Sur le chaos multiplicatif, Ann. Sci. Math. Québec, vol.9, issue.2, pp.105-150, 1985.

J. P. Kahane and J. Peyrière, Sur certaines martingales de Benoit Mandelbrot, Advances in Mathematics, vol.22, issue.2, pp.131-145, 1976.
DOI : 10.1016/0001-8708(76)90151-1

URL : http://doi.org/10.1016/0001-8708(76)90151-1

J. P. Kahane, Positive martingales and random measures, Chinese Ann, Math. Ser. B, vol.8, issue.1, pp.1-12, 1987.

A. N. Kolmogorov, Dissipation of Energy in the Locally Isotropic Turbulence, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.434, issue.1890, pp.16-18, 1941.
DOI : 10.1098/rspa.1991.0076

M. Kardar, G. Parisi, and Y. C. Zhang, Dynamic Scaling of Growing Interfaces, Physical Review Letters, vol.56, issue.9, pp.889-892, 1986.
DOI : 10.1103/PhysRevLett.56.889

A. N. Kolmogorov, A refinement of previous hypotheses concerning the local structure of turbulence, J. Fluid. Mech, vol.13, pp.83-85, 1962.

H. Kesten, Aspects of first passage percolation, Ecole d'Eté de Probabilités de Saint-Flour, XIV-1984, pp.125-264

H. Krug and H. Spohn, Kinetic roughenning of growing surfaces, Solids Far from Equilibrium, 1991.

G. F. Lawler, Intersections of Random Walks, Probability and Its Applications, Birkhauser, 1991.

M. Ledoux, Concentration of measure logarithmic Sobolev inequalities, Séminaire de Probabilités XXXIII, Lecture notes in Math, pp.120-216, 1999.

Q. Liu, On generalized multiplicative cascades, Stochastic Processes and their Applications, pp.263-286, 2000.

B. B. Mandelbrot, A possible refinement of the lognormal hypothesis concerning the distribution of energy in intermittent turbulence, Statistical Models and Turbulence Lecture Notes in Phys, pp.333-335, 1972.

B. Mandelbrot, Multiplications aléatoires et distributions invariantes par moyenne pondérée aléatoire, C RAS, vol.278, pp.289-292, 1974.

U. M. Marconi and Y. C. Zhang, Novel scaling behavior of directed polymers: disorder distribution with long tails, J. Stat. Phys, pp.61-885, 1990.

J. B. Martin, Linear growth for greedy lattice animals, Stochastic Processes and their Applications, pp.43-66, 2002.
DOI : 10.1016/S0304-4149(01)00142-9

URL : https://hal.archives-ouvertes.fr/inria-00072603

J. B. Martin, Limiting shape for directed percolation models , Annals of Probability, pp.2908-2937, 2004.

D. Nualart, The Malliavin Calculus and Related Topics, 1995.
DOI : 10.1007/978-1-4757-2437-0

A. M. Obukhov, Some specific features of atmospheric turbulence, Journal of Geophysical Research, vol.31, issue.no. 9, pp.77-81, 1962.
DOI : 10.1029/JZ067i008p03011

R. Robert, Mathématiques et turbulence, Images des mathématiques, CNRS, pp.91-100, 2004.

D. Ruelle, Chaotic Evolution and Strange Attractors, 1989.
DOI : 10.1017/CBO9780511608773

Y. Sinai, A remark concerning random walks with random potentials, Fund, Math, vol.147, pp.173-180, 1995.

R. Song and X. Y. Zhou, A remark on diffusion of directed polymers in random environments, Journal of Statistical Physics, vol.147, issue.1-2, pp.277-289, 1996.
DOI : 10.1007/BF02175566

A. S. Sznitman, Brownian Motion, Obstacles and Random media, 1998.
DOI : 10.1007/978-3-662-11281-6

V. Vargas, A local limit theorem for directed polymers in random media: the continuous and the discrete case, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.42, issue.5
DOI : 10.1016/j.anihpb.2005.08.002

URL : https://hal.archives-ouvertes.fr/hal-00004565

V. Vargas, Strong localization and macroscopic atoms for directed polymers, arXiv:math

W. Woess, Random Walks on Infinite Graphs and Groups, 2000.
DOI : 10.1017/CBO9780511470967

Y. Zhang, Non-universal roughening of kinetic self-affine interfaces, Journal de Physique, vol.51, issue.19, p.2129, 1990.
DOI : 10.1051/jphys:0199000510190212900

URL : https://hal.archives-ouvertes.fr/jpa-00212516