Uniform Poincaré inequalities for unbounded conservative spin systems: the non-interacting case

Abstract

We prove a uniform Poincaré inequality for non-interacting unbounded spin systems with a conservation law, when the single-site potential is a bounded perturbation of a convex function with polynomial growth at infinity. The result is then applied to Ginzburg–Landau processes to show diffusive scaling of the associated spectral gap.