Hydrodynamic limit of a d-dimensional exclusion process with conductances
Annales de l'I.H.P. Probabilités et statistiques, Volume 48 (2012) no. 1, p. 188-211

Fix a polynomial Φ of the form Φ(α) = α + ∑2≤jmajαk=1j with Φ'(1) > 0. We prove that the evolution, on the diffusive scale, of the empirical density of exclusion processes on 𝕋 d , with conductances given by special class of functions W, is described by the unique weak solution of the non-linear parabolic partial differential equation tρ = ∑dxkWkΦ(ρ). We also derive some properties of the operator ∑k=1dxkWk.

Étant donné un polynôme Φ de la forme Φ(α) = α + ∑2≤jmajαk=1j respectant Φ'(1) > 0, nous démontrons que l’évolution, sur une échelle diffusive, de la densité empirique des processus d’exclusion sur 𝕋 d , dont les conductances sont données par une classe spéciale de fonctions W, est décrite par l'unique solution faible de l'équation aux dérivées partielles parabolique : tρ=∑dxkWkΦ(ρ). Nous dérivons également certaines propriétés de l'opérateur ∑k=1dxkWk.

DOI : https://doi.org/10.1214/10-AIHP397
Classification:  60K35,  26A24,  35K55
Keywords: exclusion processes, random conductances, hydrodynamic limit
@article{AIHPB_2012__48_1_188_0,
     author = {Valentim, F\'abio J\'ulio},
     title = {Hydrodynamic limit of a $d$-dimensional exclusion process with conductances},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {48},
     number = {1},
     year = {2012},
     pages = {188-211},
     doi = {10.1214/10-AIHP397},
     zbl = {1254.60093},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2012__48_1_188_0}
}
Valentim, Fábio Júlio. Hydrodynamic limit of a $d$-dimensional exclusion process with conductances. Annales de l'I.H.P. Probabilités et statistiques, Volume 48 (2012) no. 1, pp. 188-211. doi : 10.1214/10-AIHP397. http://www.numdam.org/item/AIHPB_2012__48_1_188_0/

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