Convergence of ASEP to KPZ with basic coupling of the dynamics

TL;DR

This paper extends a key result by proving joint convergence of weakly asymmetric exclusion processes with multiple initial conditions, coupled via the basic coupling, to the KPZ equation driven by the same noise.

Contribution

It generalizes previous convergence results to multiple coupled initial data and analyzes properties of coupled KPZ solutions.

Findings

Joint convergence of coupled exclusion processes to KPZ with shared noise

Analysis of coupled KPZ solutions' properties

Extension of Bertini and Giacomin's seminal result

Abstract

We prove an extension of a seminal result of Bertini and Giacomin. Namely we consider weakly asymmetric exclusion processes with several distinct initial data simultaneously, then run according to the basic coupling, and we show joint convergence to the solution of the KPZ equation with the same driving noise in the limiting equation. Along the way, we analyze fine properties of nontrivially coupled solutions-in-law of KPZ-type equations.