82C22.\
    [**Keywords**]{}: [*Exclusion process; WASEP; Mixing time; Cutoff.*]{}
address:
- 'Université Paris-Dauphine, PSL Research University, Ceremade, CNRS, 75775 Paris Cedex 16, France.'
- 'IMPA, Estrada Dona Castorina 110, Rio de Janeiro, Brasil.'
author:
- Cyril Labbé
- Hubert Lacoin
bibliography:
- 'library.bib'
title: |
    Mixing time and cutoff for the weakly asymmetric\
    simple exclusion process
---

Introduction
============

The simple exclusion process is a model of statistical mechanics that provides a simplified picture for a gas of interacting particles. Particles move on a lattice, each of them performing a nearest neighbor random walk independently of the others, and interact only via the exclusion rule that prevents any two particles from sharing the same site (when a particle tries to jump on a site which is already occupied, this jump is cancelled).

In spite of its simplicity, this model displays a very rich behavior and has given rise to a rich literature both in theoretical physics and mathematics, see for instance [@KipLan; @Liggett] and references therein.

In the present paper, we study relaxation to equilibrium for a particular instance of the simple exclusion process in which the lattice is a segment of length $N$ and particles feel a bias towards the 