Title: Cutoff in the Glauber dynamics for the Gaussian free field
Abstract: The Gaussian free field (GFF) is a canonical model of random surfaces, generalizing the Brownian bridge to two dimensions. It arises naturally as the stationary solution to the stochastic heat equation with additive noise (SHE). The SHE and GFF are expected to be the universal scaling limit of many random surface evolutions arising in lattice statistical physics. We consider the mixing time (time to converge to stationarity when started out of equilibrium) for the pre-limiting object, the discrete Gaussian free field (DGFF) evolving under the Glauber dynamics. We establish that on a box of side-length $n$ in $\mathbb Z^2$, the Glauber dynamics for the DGFF exhibits the cutoff phenomenon, mixing exactly at time $\frac{2}{\pi^2} n^2 \log n$. Based on joint work with S. Ganguly.
