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

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.

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.

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

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