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A0290
Title: Convergence rates for empirical barycenters in metric spaces Authors:  Quentin Paris - NRU HSE (Russia) [presenting]
Abstract: Rates of convergence are presented for empirical barycenters of a probability measure on a metric space under general conditions. The results connect ideas from metric geometry to the theory of empirical processes and is studied in two meaningful scenarios. The first one is a geometrical constraint on the underlying space referred to as k-convexity, compatible with a positive upper curvature bound in the sense of Alexandrov. The second scenario considers the case of a non-negatively curved space on which geodesics, emanating from a barycenter, can be extended. While not restricted to this setting, our results are discussed in the context of the Wasserstein spaces.