OBABO and BAOAB schemes cannot achieve square-root of condition number acceleration for sampling with any fixed choice of step size and friction based only on curvature bounds and dimension

We prove that no fixed choice of step size and friction, based only on the curvature bounds and the dimension, achieves this acceleration: total variation mixing time lower bounds for OBABO show that ballistic cold-start mixing fails uniformly over the smooth strongly convex class

http://arxiv.org/abs/2608.25279v1