Sharp cold-start rate for nonquadratic kinetic Langevin diffusion

Determine the sharp worst-case cold-start total variation decay rate for kinetic Langevin diffusion with nonquadratic smooth strongly convex potentials.

Background

The appendix determines the optimal worst-case asymptotic total variation exponent over deterministic initial states for kinetic Langevin diffusion on Gaussian targets, showing that the critical friction achieves the square-root curvature scale.

For nonquadratic strongly convex potentials, available entropy estimates do not directly apply to point-mass initializations because such initial laws have infinite relative entropy. The corresponding sharp deterministic-start total variation rate therefore remains unresolved.