Euler hydrodynamics for attractive particle systems in random environment

Bahadoran, C.; Guiol, H.; Ravishankar, K.; Saada, E.

Annales de l'I.H.P. Probabilités et statistiques, Tome 50 (2014) no. 2, pp. 403-424.

Nous obtenons la limite hydrodynamique trempée, sous un changement d’échelle hyperbolique, pour un système de particules attractif sur $\mathbb{Z}$ en milieu aléatoire ergodique, avec un nombre borné de particules par site. Notre résultat est une loi forte des grands nombres. Nous l’illustrons sur différents exemples.

We prove quenched hydrodynamic limit under hyperbolic time scaling for bounded attractive particle systems on $\mathbb{Z}$ in random ergodic environment. Our result is a strong law of large numbers, that we illustrate with various examples.

Classification : 60K35, 82C22
Mots clés : hydrodynamic limit, attractive particle system, scalar conservation law, entropy solution, random environment, quenched disorder, generalized misanthropes and $k$-step models

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