Euler hydrodynamics for attractive particle systems in random environment

Christophe Bahadoran (1) , Hervé Guiol (2) , K. Ravishankar (3) , Ellen Saada (4)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 TIMC-IMAG - Techniques de l'Ingénierie Médicale et de la Complexité - Informatique, Mathématiques et Applications, Grenoble - UMR 5525
3 SUNY - Department of Mathematics
4 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

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

Mots clés: Hydrodynamic limit; attractive particle system; scalar conservation law; entropy solution; random environment; quenched disorder; generalized misanthropes and $k$-step models

Domaines: Probabilités [math.PR]

Christophe Bahadoran, Hervé Guiol, K. Ravishankar, Ellen Saada. Euler hydrodynamics for attractive particle systems in random environment. 2012. ⟨hal-00658559v1⟩