A universal criterion for the total-variation cutoff phenomenon in Markov diffusions with non-negative Bakry-Emery curvature (CD(0,infinity)), covering Langevin diffusions in convex potentials on Euclidean space and weighted Riemannian manifolds. The core result bounds the width of the mixing window solely in terms of the spectral gap of the generator, so that the product condition (spectral gap times mixing time diverging) implies cutoff for the entire class and arbitrary deterministic starts. The proof is elementary, resting on a new differential relation between entropy and varentropy along the semigroup, unifying and generalizing many earlier model-specific mixing-time analyses.
Salez resolves a long-standing problem in the quantitative theory of Markov processes: when does the total-variation cutoff phenomenon (an abrupt, rather than gradual, drop of the distance to equilib…