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The Glauber-Exclusion process is a superposition of a Glauber dynamics andthe Symmetric Simple Exclusion Process (SSEP) on the lattice. The model wasshown to admit a reaction-diffusion equation as the hydrodynamic limit. In thisarticle, we define a notion of temperature regimes via the reaction function inthe equation and prove cutoff in the full high-temperature regime for theattractive model in dimensions $1$ and $2$ with periodic boundary condition.Our results show that the equation in the hydrodynamic limit reflects themixing behavior of the large but finite system. Besides, cutoff is proved underthe lack of reversibility and an explicit formula for the invariant measure. Wealso provide the spectral gap and prove pre-cutoff in all dimensions. Our proofinvolves a new interpretation of attractiveness, the information percolationframework introduced by Lubetzky and Sly, anti-concentration of simple randomwalk on the lattice, and a coupling inspired by excursion theory. We hope thatthis approach can find new applications in the future.

Cutoff for the Glauber-Exclusion process in the full high-temperature regime: an information percolation approach