Abstract：

We consider the Facilitated Exclusion Process (FEP) in one dimension, which is an interacting particle system with degenerate rates. In this model, a particle could jump if and only if there is one particle in its neighbors and no particle at the target site. We derive stationary fluctuations for the FEP in the symmetric, weakly asymmetric and asymmetric cases. In particular, we observe a phase transition from the Edwards-Wilkinson universality to the Kardar-Parisi-Zhang universality. This is based on joint work with Clément Erignoux. We shall also discuss stationary fluctuations for interacting particle systems with two or more conservation laws, where a new universality class, namely the Fibonacci universality class, has been predicted by physicists.