Information percolation and the mixing times of the Glauber-Exclusion process

The Glauber-Exclusion process, an interacting particle system introduced by De Masi, Ferrari, and Lebowitz, is a superposition of a Glauber dynamics and the symmetric simple exclusion process (SSEP) on a lattice. It was shown to admit a reaction-diffusion equation as the hydrodynamic limit. In this talk, we introduce the information percolation framework invented by Lubetzky and Sly and explain how it can be used to study the mixing times of our process. After defining a notion of temperature regimes via the equation in the hydrodynamic limit, we prove that the mixing times undergo a phase transition known as cutoff for the attractive model in the high-temperature regime. Our result shows a connection between the hydrodynamic limit and the mixing behavior of the large but finite system.