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We then introduce a method for deriving lower bounds on singular value gaps for Markov processes with degenerate noise that is based on the concept of a first- and second-order collapse of the generator. It follows ideas from hypocoercivity developed in a previous series of works but is simpler and more broadly applicable. In contrast to previous results, it includes settings with non-vanishing first-order collapse, and thus applies directly to Markov chains, but also to diffusion processes and piecewise-deterministic Markov processes.
Our approach yields sharp upper and lower bounds for several classes of examples. First applications include the proof of a conjecture by Diaconis and Miclo on a square-root speed-up for lifted random walks on abelian groups, as well as bounds on relaxation times of switching flows perturbed by noise and of non-reversible diffusion processes. Joint work with Francis Lörler.
Thursday, October 22, 2026
Thursday, October 29, 2026
Thursday, November 5, 2026
Thursday, November 12, 2026
Thursday, November 19, 2026