Homogenization results for a linear dynamics in random Glauber type environment
Annales de l'I.H.P. Probabilités et statistiques, Volume 48 (2012) no. 3, p. 792-818

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.

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.

DOI : https://doi.org/10.1214/11-AIHP424
Classification:  60K35,  82C22,  82C44
Keywords: 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},
     publisher = {Gauthier-Villars},
     volume = {48},
     number = {3},
     year = {2012},
     pages = {792-818},
     doi = {10.1214/11-AIHP424},
     zbl = {1279.60123},
     mrnumber = {2976564},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 48 (2012) no. 3, pp. 792-818. doi : 10.1214/11-AIHP424. http://www.numdam.org/item/AIHPB_2012__48_3_792_0/

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