. Nous-avons-jusqu, Nous allons dans ce chapitre nous intéresserintéresserà des modèles o` u l'environnement est fourni par une percolation de sites ou d'arêtes dans Z d . Cettepremì ere section est consacréè a l'exposé de quelques notions de percolation. L'objectif est surtout d'introduire les notations que l'on utilisera par la suite dans la description des différents modèles ainsi que les outils qui nous permettront de lesétudierlesétudier. Tous les résultats présentés sont tirés de l'ouvrage de référence de Geoffrey Grimmett, Percolation, [36]. Les deux modèles (percolation de sites ou d'arêtes) sont en fait très proches, (iii) We end the paper with a short comment on the case when the environment is a general random field, not necessarily coming from site percolation. It is easy to check that Theorems 5.1 and 5.3, together with their proofs, remain valid for a stationary

O. Adelman and N. Enriquez, Random walks in random environment: What a single trajectory tells, Israel Journal of Mathematics, vol.8, issue.1, pp.205-220, 2004.

M. Aizenman and D. J. Barsky, Sharpness of the phase transition in percolation models, Communications in Mathematical Physics, vol.11, issue.3, pp.489-526, 1987.
DOI : 10.1007/BF01212322

A. Gerard-ben-arous and J. Bovier, Universality of the REM for dynamics of mean-field spin glasses

G. Ben-arous and J. , Bouchaud???s model exhibits two different aging regimes in dimension one, The Annals of Applied Probability, vol.15, issue.2, pp.1161-1192, 2005.

G. Ben-arous, . Ji?íji?í?ji?í?ern´ji?í?ern´ybovier, V. Dunlop, and . Enter, Dynamics of Trap Models, Ch. 8 dans Mathematical Statistical Physics, 2005.

G. Ben-arous and J. , Scaling limit for trap models on ??? d, The Annals of Probability, vol.35, issue.6, pp.2356-2384, 2007.

J. Bérard and A. Ramírez, Central Limit Theorem For The Excited Random Walk In Dimension \$d\geq 2\$, Electronic Communications in Probability, vol.12, issue.0, pp.303-314, 2007.
DOI : 10.1214/ECP.v12-1317

N. Berger, Limiting velocity of high-dimensional random walk in random environment, The Annals of Probability, vol.36, issue.2, pp.728-738, 2008.
DOI : 10.1214/07-AOP338

N. Berger and M. Biskup, Quenched invariance principle for simple random walk on percolation clusters. Probab. Theory Related Fields, pp.83-120, 2007.

N. Berger, N. Gantert, and Y. Peres, The speed of biased random walk on percolation clusters. Probab. Theory Related Fields, pp.221-242, 2003.

N. Berger and O. Zeitouni, A quenched invariance principle for certain ballistic random walks in i.i.d. environments. arXiv :math, 702306.

E. Bolthausen and A. Sznitman, Ten lectures on random media, volume 32 of DMV Seminar, 2002.

E. Bolthausen and O. Zeitouni, Multiscale analysis of exit distributions for random walks in random environments, Probability Theory and Related Fields, vol.164, issue.3-4, pp.581-645, 2007.

J. Bouchaud, Weak ergodicity breaking and aging in disordered systems, Journal de Physique I, vol.2, issue.9, pp.1705-1713, 1992.

A. Bovier and A. Faggionato, Spectral characterization of aging: The REM-like trap model, The Annals of Applied Probability, vol.15, issue.3, pp.1997-2037, 2005.

M. Bramson and R. Durrett, Random walk in random environment: A counterexample?, Communications in Mathematical Physics, vol.41, issue.2, pp.199-211, 1988.
DOI : 10.1007/BF01217738

J. Bricmont and A. Kupiainen, Random walks in asymmetric random environments, Communications in Mathematical Physics, vol.116, issue.2, pp.345-420, 1991.
DOI : 10.1007/BF02102067

J. Cerny, Special topics in probability -aging in dynamics of disordered systems. Notes de cours disponibles sur http

A. A. Chernov, Replication of a multicomponent chain by lightning mechanism, Biophysics, vol.12, issue.2, pp.336-341, 1967.

F. Comets, N. Gantert, and O. Zeitouni, Quenched, annealed and functional large deviations for one-dimensional random walk in random environment. Probab. Theory Related Fields, pp.65-114, 2000.

F. Comets and F. Simenhaus, Random walk delayed on percolation clusters, Journal of Applied Probability, vol.45, issue.3, 2008.

F. Comets and O. Zeitouni, A law of large numbers for random walks in random mixing environments, Ann. Probab, vol.32, issue.1B, pp.880-914, 2004.

F. Comets and O. Zeitouni, Gaussian fluctuations for random walks in random mixing environments, Israel Journal of Mathematics, vol.27, issue.1, pp.87-114, 2005.

P. G. De-gennes, La percolation : un concept unifiacateur, La Recherche, vol.7, pp.919-927, 1976.

P. G. De-gennes, La capture d'une fourmi par despì eges sur un amas de percolation, Comptes Rendues de l'Académie des Sciences, pp.881-884, 1983.

A. De-masi, P. A. Ferrari, S. Goldstein, and W. D. Wick, An invariance principle for reversible Markov processes. Applications to random motions in random environments, Journal of Statistical Physics, vol.38, issue.1, pp.3-4787, 1989.
DOI : 10.1007/BF01041608

P. Diaconis, Recent progress on de Finetti's notions of exchangeability, Bayesian statistics Oxford Sci. Publ, pp.111-125, 1987.

G. Peter, J. L. Doyle, and . Snell, Random walks and electric networks, Carus Mathematical Monographs. Mathematical Association of America, vol.22, 1984.

R. Durrett, Multidimensional RWRE with Subclassical Limiting Behavior, Random media, pp.109-119, 1985.

N. Enriquez and C. Sabot, Edge oriented reinforced random walks and RWRE, Comptes Rendus Mathematique, vol.335, issue.11, pp.941-946, 2002.

N. Enriquez and C. Sabot, Random walks in a Dirichlet environment, Electron . J. Probab, vol.11, issue.31, pp.802-817, 2006.

N. Enriquez, C. Sabot, and O. Zindy, Aging and quenched localization for one-dimensional random walks in random environment in the sub-ballistic regime, Bulletin de la Soci&#233;t&#233; math&#233;matique de France, vol.137, issue.3

L. Goergen, Limit velocity and zero???one laws for diffusions in random environment, The Annals of Applied Probability, vol.16, issue.3, pp.1086-1123, 2006.

A. Greven, . Frank, and . Hollander, Large Deviations for a Random Walk in Random Environment, The Annals of Probability, vol.22, issue.3, pp.1381-1428, 1994.

G. R. Grimmett, H. Kesten, and Y. Zhang, Random walk on the infinite cluster of the percolation model. Probab. Theory Related Fields, pp.33-44, 1993.

J. Jacod and A. N. Shiryaev, Limit theorems for stochastic processes, of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 1987.

A. Steven and . Kalikow, Generalized random walk in a random environment, Ann. Probab, vol.9, issue.5, pp.753-768, 1981.

H. Kesten, M. V. Kozlov, and F. Spitzer, A limit law for random walk in a random environment, Compositio Math, vol.30, pp.145-168, 1975.

H. Kesten, The Limit Points of a Normalized Random Walk, The Annals of Mathematical Statistics, vol.41, issue.4, pp.1173-1205, 1970.

C. Kipnis and S. R. Varadhan, Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions, Communications in Mathematical Physics, vol.28, issue.1, pp.1-19, 1986.
DOI : 10.1007/BF01210789

S. M. Kozlov, The method of averaging and walks in inhomogeneous environments, Russian Mathematical Surveys, vol.40, issue.2, pp.73-145, 1985.

P. Mathieu, Quenched Invariance Principles for Random Walks with??Random Conductances, Journal of Statistical Physics, vol.129, issue.2, pp.1025-1046, 2008.

P. Mathieu and A. Piatnitski, Quenched invariance principles for random walks on percolation clusters, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.463, issue.2085, pp.2287-2307, 2007.

P. Mathieu, Zero white noise limit through Dirichlet forms, with application to diffusions in a random medium. Probab. Theory Related Fields, pp.549-580, 1994.

M. V. Men and ?. Shikov, Coincidence of critical points in percolation problems, Dokl. Akad. Nauk SSSR, vol.288, issue.6, pp.1308-1311, 1986.

S. P. Meyn and R. L. Tweedie, Markov chains and stochastic stability. Communications and Control Engineering Series, 1993.

C. Monthus, Nonlinear response of the trap model in the aging regime: Exact results in the strong-disorder limit, Physical Review E, vol.69, issue.2, p.26103, 2004.

Y. Peres, Probability on Trees: An Introductory Climb, Lecture Notes in Math, vol.1717, pp.193-280, 1997.

S. Popov and M. Vachkovskaia, Random Walk Attracted by Percolation Clusters, Electronic Communications in Probability, vol.10, issue.0, pp.263-272, 2005.

T. Svetlozar, L. Rachev, and . Rüschendorf, Mass transportation problems, Probability and its Applications, 1998.

F. Rassoul-agha, The point of view of the particle on the law of large numbers for random walks in a mixing random environment, The Annals of Probability, vol.31, issue.3, pp.1441-1463, 2003.

F. Rassoul-agha and T. Seppäläinen, Almost sure functional central limit theorem for ballistic random walk in random environment, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.45, issue.2
DOI : 10.1214/08-AIHP167

F. Rassoul-agha and T. Seppäläinen, Almost sure functional central limit theorem for non-nestling random walk in random environment

F. Rassoul-agha and T. Seppäläinen, Quenched invariance principle for multidimensional ballistic random walk in a random environment with a forbidden direction, The Annals of Probability, vol.35, issue.1, pp.1-31, 2007.

C. Rau, Sur le nombre de points visit??s par une marche al??atoire sur un amas infini de percolation, Bulletin de la Soci&#233;t&#233; math&#233;matique de France, vol.135, issue.1, pp.135-169, 2007.

P. Révész, Random walk in random and non-random environments, Pte. Ltd, 2005.

J. M. Rosenbluth, Quenched large deviations for multidimensional random walk in random environment : a variational formula

L. Shen, Asymptotic properties of certain anisotropic walks in random media, The Annals of Applied Probability, vol.12, issue.2, pp.477-510, 2002.

V. Sidoravicius and A. Sznitman, Quenched invariance principles for walks on clusters of percolation or among random conductances. Probab. Theory Related Fields, pp.219-244, 2004.

F. Simenhaus, Asymptotic direction for random walks in random environments, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.43, issue.6, pp.751-761, 2007.

F. Solomon, Random Walks in a Random Environment, The Annals of Probability, vol.3, issue.1, pp.1-31, 1975.

A. Sznitman, On a Class Of Transient Random Walks in Random Environment, The Annals of Probability, vol.29, issue.2, pp.724-765, 2001.

A. Sznitman, An effective criterion for ballistic behavior of random walks in random environment. Probab. Theory Related Fields, pp.509-544, 2002.

A. Sznitman, On new examples of ballistic random walks in random environment, The Annals of Probability, vol.31, issue.1, pp.285-322, 2003.

A. Sznitman, On the Anisotropic Walk on the Supercritical Percolation Cluster, Communications in Mathematical Physics, vol.240, issue.1-2, pp.123-148, 2003.

A. Sznitman and O. Zeitouni, An invariance principle for isotropic diffusions in random environment, Inventiones mathematicae, vol.164, issue.3, pp.455-567, 2006.

A. Sznitman and M. Zerner, A law of large numbers for random walks in random environment, Ann. Probab, vol.27, issue.4, pp.1851-1869, 1999.

D. E. Temkin, One-dimensional random walks in a two-component chain, Dokl. Akad. Nauk SSSR, vol.206, pp.27-30, 1972.

H. Thorisson, Coupling, stationarity, and regeneration. Probability and its Applications, 2000.

S. R. Varadhan, Large deviations for random walks in a random environment, Communications on Pure and Applied Mathematics, vol.29, issue.8, pp.1222-1245, 2003.
DOI : 10.1002/cpa.10093

C. Villani, Topics in optimal transportation, Graduate Studies in Mathematics, vol.58, 2003.
DOI : 10.1090/gsm/058

A. Yilmaz, Quenched large deviations for random walk in a random environment, Communications on Pure and Applied Mathematics, vol.26, issue.4
DOI : 10.1002/cpa.20283

O. Zeitouni, Part II: Random Walks in Random Environment, Lectures on probability theory and statistics, pp.189-312, 2004.

P. W. Martin and . Zerner, Lyapounov exponents and quenched large deviations for multidimensional random walk in random environment, Ann. Probab, vol.26, issue.4, pp.1446-1476, 1998.

P. W. Martin and . Zerner, A non-ballistic law of large numbers for random walks in i.i.d. random environment, Electron. Comm. Probab, vol.7, pp.191-197, 2002.

P. W. Martin and . Zerner, The zero-one law for planar random walks in i.i.d. random environments revisited, Electron. Comm. Probab, vol.12, pp.326-335, 2007.

P. W. Martin, F. Zerner, and . Merkl, A zero-one law for planar random walks in random environment, Ann. Probab, vol.29, issue.4, pp.1716-1732, 2001.