Scaling limit of stationary coupled Sasamoto-Spohn models

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.

Riemann surfaces for KPZ with periodic boundaries

“…Non-linear fluctuating hydrodynamics [12,13] predicts various universality classes for the fluctuations of normal modes, including diffusive and KPZ fluctuations, and more generally a whole family [509] with dynamical exponent z given by a ratio of two consecutive Fibonacci numbers. At the level of microscopic models, coupled Burgers' equations have been proved in some cases [510][511][512][513][514].…”