S. C. Song : Type spaces and Wasserstein spaces

Posted by , part of the Logic Seminar.

At

March 29, 2011, 3 p.m.

In

SEO 612

Abstract

Ben Yaacov showed that types (over parameters) in the theory of atomless random variable structures (ARV) correspond precisely to (conditional) distributions in probability. Moreover, the logic topology on types corresponds to the topology of weak convergence of distributions. During this talk, I will define a new metric d* between types which is equivalent to the usual d-metric in continuous model theory. Then I will show the type space under the d*-metric is isometric to the Wasserstein space, the space of distributions on [0, 1]^n, under the Wasserstein distance. After this, I will show how the Kantorovich-Rubinstein duality formula from optimal transport theory yields a formula for the d*-metric. Finally, using results from continuous logic, I will generalize some results in optimal transport theory.

Logic tea at 2:30pm in SEO 300.