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math.ST2019★ 18 cited
Fast convergence of empirical barycenters in Alexandrov spaces and the Wasserstein space
Thibaut Le Gouic, Quentin Paris, Philippe Rigollet +1
This work establishes fast rates of convergence for empirical barycenters over a large class of geodesic spaces with curvature bounds in the sense of Alexandrov. More specifically,…
math.MG2019★ 1 cited
A note on flatness of non separable tangent cone
Thibaut Le Gouic
Given a probability measure P on an Alexandrov space S with curvature bounded below, we prove that the support of the pushforward of P on the tangent cone at its (exponential) bary…