Scaling limit of stationary coupled Sasamoto-Spohn models

TL;DR

This paper introduces stationary coupled Sasamoto-Spohn models and proves their convergence to coupled Burgers equations in the weakly asymmetric regime, providing a new approach via a second order Boltzmann-Gibbs principle.

Contribution

It establishes the scaling limit of coupled Sasamoto-Spohn models to coupled Burgers equations without spectral gap estimates, and characterizes all stationary coupled Burgers systems as limits.

Findings

Models converge to coupled Burgers equations in the weakly asymmetric regime

Any stationary coupled Burgers system satisfying the trilinear condition can be obtained as a limit

A new proof technique using a second order Boltzmann-Gibbs principle

Abstract

We introduce a family of stationary coupled Sasamoto-Spohn models and show that, in the weakly asymmetric regime, they converge to the energy solution of coupled Burgers equations. Moreover, we show that any system of coupled Burgers equations satisfying the so-called trilinear condition ensuring stationarity can be obtained as the scaling limit of a suitable system of coupled Sasamoto-Spohn models. The core of our proof, which avoids the use of spectral gap estimates, consists in a second order Boltzmann-Gibbs principle for the discrete model.