Hydrodynamic limit of the directed exclusion process

TL;DR

This paper establishes the Euler hydrodynamic limit for the directed exclusion process, a one-dimensional particle system with asymmetric dynamics, using a novel multi-process coupling method.

Contribution

It introduces a new coupling approach to prove hydrodynamic limits for DEP, highlighting macroscopic stability and attractiveness properties.

Findings

Proves the Euler hydrodynamic limit for DEP

Develops an explicit multi-process coupling technique

Discusses open questions about DEP

Abstract

We derive the Euler (hyperbolic) hydrodynamic limit for the directed exclusion process (DEP), a one-dimensional conservative interacting particle system that preserves particle-hole symmetry while breaking left-right symmetry. The proof relies on an explicit multi-process coupling, which guarantees a strong form of attractiveness and macroscopic stability for the particle system. Further open questions about DEP are briefly discussed.