Corrigendum to: Phase transition in equilibrium fluctuations of symmetric slowed exclusion

TL;DR

This paper corrects the test function space for Ornstein-Uhlenbeck processes related to symmetric slowed exclusion, establishing invariance and proving existence and uniqueness of these processes.

Contribution

It introduces the correct test function space for these processes and demonstrates invariance, ensuring their well-posedness.

Findings

Established the correct test function space for the processes

Proved invariance under a second order operator

Confirmed existence and uniqueness of the Ornstein-Uhlenbeck processes

Abstract

We present the correct space of test functions for the Ornstein-Uhlenbeck processes defined in \cite{fgn2}. Under these new spaces, an invariance with respect to a second order operator is shown, granting the existence and uniqueness of those processes. Moreover, we detail how to prove some properties of the semi-groups, which are required in the proof of uniqueness.