Scaling of the Sasamoto-Spohn model in equilibrium

TL;DR

This paper proves that the Sasamoto-Spohn model converges to the stochastic Burgers equation in equilibrium, using a novel approach that avoids spectral gap arguments and relies on the Boltzmann-Gibbs principle.

Contribution

It establishes the convergence of the Sasamoto-Spohn model to the stochastic Burgers equation without spectral gap assumptions, advancing the theoretical understanding of these models.

Findings

Convergence of the Sasamoto-Spohn model to the stochastic Burgers equation.

Application of the second order Boltzmann-Gibbs principle in the proof.

Elimination of spectral gap argument in the convergence proof.

Abstract

We prove the convergence of the Sasamoto-Spohn model in equilibrium to the energy solution of the stochastic Burgers equation on the whole line. The proof, which relies on the second order Boltzmann-Gibbs principle, follows the approach of \cite{GJS} and does not use any spectral gap argument.