Abstract: In joint work with Zemer Kosloff, we will discuss the dynamical properties of a seemingly innocuous perturbation of a sequence of independent and identically distributed (iid) coin-flips to one that is no longer stationary. In the stationary case, Ornstein proved that iid systems are completely classified up to isomorphism by their Shannon entropy. We will find that in the nonstationary case, the usual entropy theory no longer applies, but we will recover an explicit version of the Sinai factor theorem that allows us to generate iid randomness from a nonstationary source.

Abstract: In this talk I will discuss a new family of metrics (called Disintegrated Monge-Kantorovich metrics) which we introduced on spaces of probability measures on a metric fiber bundle with fixed base marginal, and the geometric properties of these metrics. Our metrics include the linearized optimal transport metric and admit an isometric embedding of the sliced Wasserstein metrics. I will also discuss some results on related barycenter problems. This talk is based on joint work with Asuka Takatsu (Tokyo Metropolitan U)