Probability Seminar: Duality between Total Variation and Equivalence Couplings

Seminar | April 12 | 3:10-4 p.m. | 340 Evans Hall

Speaker/Performer:  Adam Jaffe, UC Berkeley

Sponsor:  Department of Statistics

A classical lemma (sometimes attributed to Doeblin) relates the total variation distance between two probability measures to the minimal probability that two random variables with these laws can be made to disagree under all possible couplings. This talk focuses on a generalization of this problem where the random variables are asked, instead, to be equivalent under an arbitrary equivalence relation. The resulting Doeblin-type duality constitutes a form of Kantorovich duality for a class of cost functions which are highly irregular from the point of view of the standard Monge-Kantorovich theory of optimal transport. These results recover several classical and recent results, and have novel applications in random variable simulation, determinantal point processes, and stochastic calculus.

Event Contact:  lfzhang@berkeley.edu, 510-000000000

Access Coordinator:  Lingfu Zhang,  lfzhang@berkeley.edu,  510-000-0000