# Derivation of viscous Burgers equations from weakly asymmetric exclusion processes

## TL;DR

This paper demonstrates that the density evolution in weakly asymmetric exclusion processes converges to a viscous Burgers equation in the diffusive time-scale across all dimensions.

## Contribution

It establishes a rigorous derivation of viscous Burgers equations from weakly asymmetric exclusion processes for small initial perturbations.

## Key findings

- Density defect evolves as viscous Burgers equation
- Valid in all spatial dimensions
- Applicable in the diffusive time-scale

## Abstract

We consider weakly asymmetric exclusion processes whose initial density profile is a small perturbation of a constant. We show that in the diffusive time-scale, in all dimensions, the density defect evolves as the solution of a viscous Burgers equation.