A. Abdulle, M. J. Grote, and C. Stohrer, Finite element heterogeneous multiscale method for the wave equation: long-time effects, Multiscale Model. Simul, vol.12, issue.3, pp.1230-1257, 2014.
DOI : 10.1137/13094195x

URL : https://hal.archives-ouvertes.fr/hal-01111169

A. Abdulle and T. Pouchon, A Priori Error Analysis of the Finite Element Heterogeneous Multiscale Method for the Wave Equation over Long Time, SIAM J. Numer. Anal, vol.54, issue.3, pp.1507-1534, 2016.

M. Aizenman and S. Warzel, Random operators, Disorder effects on quantum spectra and dynamics, vol.168, 2015.

G. Allaire, M. Briane, and M. Vanninathan, A comparison between two-scale asymptotic expansions and Bloch wave expansions for the homogenization of periodic structures, SeMA Journal, pp.1-23, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01215580

G. Allaire and C. Conca, Analyse asymptotique spectrale de l'´ equation des ondes, Complétude du spectre de Bloch. C. R. Acad. Sci. Paris Sér. I Math, vol.321, issue.5, pp.557-562, 1995.
DOI : 10.1016/s0764-4442(97)86972-8

G. Allaire and C. Conca, Analyse asymptotique spectrale de l'´ equation des ondes. Homogénéisation par ondes de Bloch, C. R. Acad. Sci. Paris Sér. I Math, vol.321, issue.3, pp.293-298, 1995.
DOI : 10.1016/s0764-4442(97)86972-8

G. Allaire, M. Palombaro, and J. Rauch, Diffractive behavior of the wave equation in periodic media: weak convergence analysis, Ann. Mat. Pura Appl, vol.188, issue.4, pp.561-589, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00784060

G. Allaire, M. Palombaro, and J. Rauch, Diffractive geometric optics for Bloch wave packets, Arch. Ration. Mech. Anal, vol.202, issue.2, pp.373-426, 2011.
DOI : 10.1007/s00205-011-0452-9

URL : http://www.math.lsa.umich.edu/~rauch/wkbbloch24.pdf

S. Armstrong, A. Gloria, and T. Kuusi, Bounded Correctors in Almost Periodic Homogenization, Arch. Ration. Mech. Anal, vol.222, issue.1, pp.393-426, 2016.
DOI : 10.1007/s00205-016-1004-0

URL : https://hal.archives-ouvertes.fr/hal-01230991

S. Armstrong, T. Kuusi, and J. Mourrat, The additive structure of elliptic homogenization, Invent. Math, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01483468

S. N. Armstrong and C. K. Smart, Quantitative stochastic homogenization of convex integral functionals, Ann. Sci. ´ Ec. Norm. Supér, vol.49, issue.4, pp.423-481, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01483473

P. Bella, B. Fehrman, J. Fischer, and F. Otto, Stochastic homogenization of linear elliptic equations: Higher-order error estimates in weak norms via second-order correctors, 2016.

S. Brahim-otsmane, G. A. Francfort, and F. Murat, Correctors for the homogenization of the wave and heat equations, J. Math. Pures Appl, vol.71, issue.9, pp.197-231, 1992.

T. Chen, Localization lengths and Boltzmann limit for the Anderson model at small disorders in dimension 3, J. Stat. Phys, vol.120, issue.1-2, pp.279-337, 2005.

C. Conca, R. Orive, and M. Vanninathan, On Burnett coefficients in periodic media, J. Math. Phys, vol.47, issue.3, p.32902, 2006.
DOI : 10.1063/1.2179048

C. Conca and M. Vanninathan, Homogenization of periodic structures via Bloch decomposition, SIAM J. Appl. Math, vol.57, issue.6, pp.1639-1659, 1997.
DOI : 10.1137/s0036139995294743

T. Dohnal, A. Lamacz, and B. Schweizer, Bloch-wave homogenization on large time scales and dispersive effective wave equations, Multiscale Model. Simul, vol.12, issue.2, pp.488-513, 2014.

T. Dohnal, A. Lamacz, and B. Schweizer, Dispersive homogenized models and coefficient formulas for waves in general periodic media, Asymptot. Anal, vol.93, issue.1-2, pp.21-49, 2015.

M. Duerinckx and A. Gloria, Weighted functional inequalities: Concentration properties

M. Duerinckx and A. Gloria, Weighted functional inequalities: Constructive approach
URL : https://hal.archives-ouvertes.fr/hal-01633041

M. Duerinckx, A. Gloria, and C. Shirley, Approximate spectral theory and asymptotic ballistic transport of quantum waves

A. Figotin and A. Klein, Localization of classical waves. I. Acoustic waves, Comm. Math. Phys, vol.180, issue.2, pp.439-482, 1996.

G. A. Francfort and F. Murat, Oscillations and energy densities in the wave equation, Comm. Partial Differential Equations, vol.17, pp.1785-1865, 1992.

A. Gloria and Z. Habibi, Reduction in the resonance error in numerical homogenizaton II: correctors and extrapolation, Foundations of Computational Mathematics, vol.16, pp.217-296, 2016.

A. Gloria, S. Neukamm, and F. Otto, Quantification of ergodicity in stochastic homogenization: optimal bounds via spectral gap on Glauber dynamics, Invent. Math, vol.199, issue.2, pp.455-515, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01093405

A. Gloria, S. Neukamm, and F. Otto, A regularity theory for random elliptic operators, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01093368

A. Gloria, S. Neukamm, and F. Otto, Quantitative stochastic homogenization for correlated fields, 2014.

A. Gloria and F. Otto, The corrector in stochastic homogenization: optimal rates, stochastic integrability, and fluctuations, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01230985

A. Gloria and F. Otto, Quantitative results on the corrector equation in stochastic homogenization, J. Eur. Math. Soc. (JEMS)
URL : https://hal.archives-ouvertes.fr/hal-01093381

A. Gloria and F. Otto, An optimal variance estimate in stochastic homogenization of discrete elliptic equations, Ann. Probab, vol.39, issue.3, pp.779-856, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00383953

A. Gloria and F. Otto, An optimal error estimate in stochastic homogenization of discrete elliptic equations, Ann. Appl. Probab, vol.22, issue.1, pp.1-28, 2012.
URL : https://hal.archives-ouvertes.fr/inria-00457020

Y. Gu, High order correctors and two-scale expansions in stochastic homogenization, 2016.

S. M. Kozlov, Averaging of differential operators with almost periodic rapidly oscillating coefficients. Mat. Sb, vol.317, pp.199-217, 1978.

A. Lamacz, Dispersive effective models for waves in heterogeneous media, Math. Models Methods Appl. Sci, vol.21, issue.9, pp.1871-1899, 2011.

A. Naddaf and T. Spencer, Estimates on the variance of some homogenization problems, 1998.

G. Papanicolaou, Mathematical problems in geophysical wave propagation, Proceedings of the International Congress of Mathematicians, vol.I, pp.403-427, 1998.

L. Ryzhik, G. Papanicolaou, and J. B. Keller, Transport equations for elastic and other waves in random media, Wave Motion, vol.24, issue.4, pp.327-370, 1996.
DOI : 10.1016/s0165-2125(96)00021-2

URL : http://math.stanford.edu/~papanico/pubftp/TRANSPORT.pdf

F. Santosa and W. W. Symes, A dispersive effective medium for wave propagation in periodic composites, SIAM J. Appl. Math, vol.51, issue.4, pp.984-1005, 1991.
DOI : 10.1137/0151049

P. Stollmann, Caught by disorder, Bound states in random media, vol.20, 2001.
DOI : 10.1007/978-1-4612-0169-4

, Calais, France E-mail address: antoine.benoit@univ-littoral.fr (Antoine Gloria) Sorbonne Université, Laboratoire Jacques-Louis Lions, F-75005