Derivation of the Stochastic Burgers equation from the WASEP

TL;DR

This paper provides a straightforward proof of the Boltzmann-Gibbs Principle, demonstrating that the equilibrium fluctuations of the Weakly Asymmetric Simple Exclusion Process (WASEP) are governed by the Stochastic Burgers equation in the critical asymmetry regime.

Contribution

It offers a simplified proof of the Boltzmann-Gibbs Principle crucial for deriving the Stochastic Burgers equation from WASEP.

Findings

Equilibrium fluctuations of WASEP are described by the Stochastic Burgers equation.

The proof of the Boltzmann-Gibbs Principle is simplified.

The results apply specifically in the critical asymmetry regime.

Abstract

In these notes we give a simple proof of the second-order Boltzmann-Gibbs Principle, which is the main tool in order to prove that the equilibrium fluctuations of the WASEP are given, in the regime of the critical strength asymmetry, by the Stochastic Burgers equation.