Cold-start lower bound for Metropolized OBABO

Determine whether Metropolized OBABO satisfies the conjectured cold-start mixing-time lower bound uniformly over the class of smooth strongly convex potentials, despite exact preservation of the kinetic Langevin target measure.

Background

Unlike unadjusted OBABO, Metropolized OBABO preserves the Gibbs measure exactly, and rejection causes a momentum flip. These changes alter the deterministic dynamics and may destroy or redirect the attracting cycles used to prove metastability for the unadjusted chain.

The paper therefore identifies Metropolized OBABO as a decisive test of whether the proposed general lower-bound principle survives Metropolis correction or whether rejection and momentum reversal can enable accelerated mixing.