Euler hydrodynamics for attractive particle systems in random environment

TL;DR

This paper establishes a strong law of large numbers for the hydrodynamic behavior of attractive particle systems in random environments, providing a rigorous foundation for understanding their macroscopic limits.

Contribution

It proves the quenched hydrodynamic limit under hyperbolic scaling for bounded attractive particles in ergodic random environments, a novel result in this context.

Findings

Hydrodynamic limit proven for attractive particle systems in random environments

Strong law of large numbers established for these systems

Illustrated with various examples

Abstract

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.