Date: 28 April 2025 - 02 May 2025
We will focus on weakly asymmetric exclusion processes on the line or half-line, and investigate their fluctuations out of equilibrium. We will review the various tools used in proving convergence to the KPZ equation in the strategy initiated in [Bertini-Giacomin ‘97] and discuss how they can be adapted to the singular initial condition that arises when one considers fluctuations of the facilitated exclusion process at the interface.