Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Euler hydrodynamics for attractive particle systems in random environment

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

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Abstract

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.

Résumé

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.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist. Volume 50, Number 2 (2014), 403-424.

Dates
First available in Project Euclid: 26 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1395856133

Digital Object Identifier
doi:10.1214/12-AIHP510

Mathematical Reviews number (MathSciNet)
MR3189077

Zentralblatt MATH identifier
1294.60116

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82C22: Interacting particle systems [See also 60K35]

Keywords
Hydrodynamic limit Attractive particle system Scalar conservation law Entropy solution Random environment Quenched disorder Generalized misanthropes and $k$-step models

Citation

Bahadoran, C.; Guiol, H.; Ravishankar, K.; Saada, E. Euler hydrodynamics for attractive particle systems in random environment. Ann. Inst. H. Poincaré Probab. Statist. 50 (2014), no. 2, 403--424. doi:10.1214/12-AIHP510. https://projecteuclid.org/euclid.aihp/1395856133


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