On considère un système d'équations differentielles linéaires couplées conservant une certaine énergie et l'on perturbe ce système par une dynamique de type Glauber dont l'intensité varie aléatoirement site par site. Nous prouvons les limites hydrodyanmiques pour ce système non réversible en milieu aléatoire. Le coefficient de diffusion dépend de l'aléa uniquement par sa loi. Nous étudions aussi le coefficient de diffusion défini par la formule de Green-Kubo et montrons la convergence de celle-ci vers un coefficient de diffusion homogénéisé.
We consider an energy conserving linear dynamics that we perturb by a Glauber dynamics with random site dependent intensity. We prove hydrodynamic limits for this non-reversible system in random media. The diffusion coefficient turns out to depend on the random field only by its statistics. The diffusion coefficient defined through the Green-Kubo formula is also studied and its convergence to some homogenized diffusion coefficient is proved.
Mots clés : hydrodynamic limits, random media, Green-Kubo formula, homogenization
@article{AIHPB_2012__48_3_792_0, author = {Bernardin, C\'edric}, title = {Homogenization results for a linear dynamics in random {Glauber} type environment}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {792--818}, publisher = {Gauthier-Villars}, volume = {48}, number = {3}, year = {2012}, doi = {10.1214/11-AIHP424}, mrnumber = {2976564}, zbl = {1279.60123}, language = {en}, url = {http://www.numdam.org/articles/10.1214/11-AIHP424/} }
TY - JOUR AU - Bernardin, Cédric TI - Homogenization results for a linear dynamics in random Glauber type environment JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2012 SP - 792 EP - 818 VL - 48 IS - 3 PB - Gauthier-Villars UR - http://www.numdam.org/articles/10.1214/11-AIHP424/ DO - 10.1214/11-AIHP424 LA - en ID - AIHPB_2012__48_3_792_0 ER -
%0 Journal Article %A Bernardin, Cédric %T Homogenization results for a linear dynamics in random Glauber type environment %J Annales de l'I.H.P. Probabilités et statistiques %D 2012 %P 792-818 %V 48 %N 3 %I Gauthier-Villars %U http://www.numdam.org/articles/10.1214/11-AIHP424/ %R 10.1214/11-AIHP424 %G en %F AIHPB_2012__48_3_792_0
Bernardin, Cédric. Homogenization results for a linear dynamics in random Glauber type environment. Annales de l'I.H.P. Probabilités et statistiques, Tome 48 (2012) no. 3, pp. 792-818. doi : 10.1214/11-AIHP424. http://www.numdam.org/articles/10.1214/11-AIHP424/
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