Hydrodynamic limit of the directed exclusion process
Probability
2026-04-24 v2
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.
Keywords
Cite
@article{arxiv.2604.08154,
title = {Hydrodynamic limit of the directed exclusion process},
author = {Ellen Saada and Federico Sau and Assaf Shapira},
journal= {arXiv preprint arXiv:2604.08154},
year = {2026}
}