Speaker: Clare Wickman (UMCP)

Title: Probabilistic Frames and Optimal Transport


Probabilistic frames are an extension of frames for Euclidean space to probability measures with finite second moment on that space . While many of the familiar results from finite frame theory are retrievable in this setting, new tools also become available. In particular, one can impose a metric, the 2-Wasserstein distance, on this space. The construction of this metric and of geodesics in this space relies on characterization of solutions to the Monge-Kantorovich optimal transport problem. In this talk, we shall describe probabilistic frames in detail, explore the nature of solutions to the Monge-Kantorovich problem in the context of probabilistic frames, and present some initial results on constructions of probabilistic frames using optimal transport.