V. V. Anshelevich, K. M. Khanin, and Y. G. Sina?-i, Symmetric random walks in random environments, Communications in Mathematical Physics, vol.113, issue.3, pp.449-470, 1982.
DOI : 10.1007/BF01208724

M. T. Barlow and J. Deuschel, Invariance principle for the random conductance model with unbounded conductances, The Annals of Probability, vol.38, issue.1, pp.234-276, 2010.
DOI : 10.1214/09-AOP481

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

M. Biskup and T. M. Prescott, Functional CLT for Random Walk Among Bounded Random Conductances, Electronic Journal of Probability, vol.12, issue.0, pp.1323-1348, 2007.
DOI : 10.1214/EJP.v12-456

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.3-4, 1989.
DOI : 10.1007/BF01041608

]. R. Du and . Durrett, Probability: theory and examples, 1996.

A. Gloria, Numerical approximation of effective coefficients in stochastic homogenization of discrete elliptic equations. M2AN, pp.1-38, 2012.
URL : https://hal.archives-ouvertes.fr/inria-00510514

]. A. Go10a, F. Gloria, and . Otto, An optimal variance estimate in stochastic homogenization of discrete elliptic equations, Ann. Probab, vol.39, issue.3, pp.779-856, 2011.

A. Gloria and F. Otto, An optimal error estimate in stochastic homogenization of discrete elliptic equations, The Annals of Applied Probability, vol.22, issue.1, pp.1-28
DOI : 10.1214/10-AAP745

URL : https://hal.archives-ouvertes.fr/inria-00457020

A. Gloria and J. Mourrat, Spectral measure and approximation of homogenized coefficients . Probab. Theory Related Fields
URL : https://hal.archives-ouvertes.fr/inria-00510513

W. Hebisch and L. Saloff-coste, Gaussian Estimates for Markov Chains and Random Walks on Groups, The Annals of Probability, vol.21, issue.2, pp.673-709, 1993.
DOI : 10.1214/aop/1176989263

K. Klenke and . Wahrscheinlichkeitstheorie, English version appeared as: Probability theory. A comprehensive course, 2006.

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. Kozlovko87-]-s, . Kozlovkü83-]-r, and . Künnemann, The averaging method and walks in inhomogeneous environments Averaging of difference schemes The diffusion limit for reversible jump processes on Z d with ergodic random bond conductivities, English transl.: Russian Math. Surveys, pp.61-120, 1983.

P. Mathieu, Quenched Invariance Principles for Random Walks with??Random Conductances, Journal of Statistical Physics, vol.129, issue.2, pp.1025-1046, 2008.
DOI : 10.1007/s10955-007-9465-z

P. Mathieu and A. Piatnitski, Quenched invariance principles for random walks on percolation clusters, Proc. R. Soc. A, pp.2287-2307, 2007.
DOI : 10.1098/rspa.2007.1876

J. Mourrat, Variance decay for functionals of the environment viewed by the particle, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.47, issue.1, pp.294-327, 2011.
DOI : 10.1214/10-AIHP375

URL : https://hal.archives-ouvertes.fr/hal-01271688

G. C. Papanicolaou and S. R. Varadhan, Boundary value problems with rapidly oscillating random coefficients, Random fields, pp.835-873, 1979.

G. Papanicolaou, Diffusions and random walks in random media, The mathematics and physics of disordered media, pp.391-399, 1983.
DOI : 10.1007/BF01646091

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.

A. Gloria, S. Project-team, U. Painlevé, I. 8524, and . Lille, Nord Europe & Université Lille 1, Villeneuve d'Ascq, France E-mail address: antoine.gloria@inria.fr (Jean-Christophe Mourrat) EPFL, institut de mathématiques, station 8, Lausanne, 1015.