Rapid mixing for Gibbs measures in Riemannian manifolds
Ángela Capel, Marco Castrillón-López, Sofyan Iblisdir, Angelo Lucia, Pablo Páez-Velasco, David Pérez-García
Abstract
Langevin dynamics on Riemannian manifolds is analyzed. Conditions ensuring the existence of a suitable logarithmic Sobolev inequality (rapid mixing to the Gibbs measure) are identified. These conditions involve the curvature of the manifold, the inverse temperature, escaping directions from saddle points, and exclude barren plateaus and spurious local minima. We show that when these conditions are met, mixing times polynomial in the dimension of the manifold are achievable. This result is obtained through a relation between Langevin processes in the domain and in the image of a Riemannian submersion. Such a relation can be of independent interest.
Topics
Classified with taxonomy v2 on Wed, 2 Sept 2026.