Corrigendum to “Phase transition in equilibrium fluctuations of symmetric slowed exclusion” [Stochastic Process. Appl. 123(12) (2013) 4156–4185]

We present the correct space of test functions for the Ornstein–Uhlenbeck processes defined in Franco et al. (2013). 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 semigroups, which are required in the proof of uniqueness.