Logic Seminar
S. C. Song
UIUC
Type spaces and Wasserstein spaces
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.
Tuesday March 29, 2011 at 3:00 PM in SEO 612