Spectral gap and cutoff phenomenon for the Gibbs sampler of $\nabla \phi$ interfaces with convex potential

Pietro Caputo, Cyril Labbé, Hubert Lacoin

We consider the Gibbs sampler, or heat bath dynamics associated to log-concave measures on ${\mathbb{R}}^N$ describing $\nabla \phi$ interfaces with convex potentials. Under minimal assu…