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홈 > 학술정보 >학술행사 > 세미나
KAIST PDE 세미나

Title
Barycentre problems and geometry of the space of probability measures.
Speaker
Young-Heon Kim   (UBC, Canada )
Date
2017-08-25 17:00:00
Host
KAIST
Place
(E2) Room 3221
Abstract
Barycentre is the geometric mean of a distribution on a metric space; it is a point that minimizes its average distance squared to the given distribution. Such a point is highly non-unique in general, though we have uniqueness when the underlying space is the Euclidean space or more generally a space of nonpositive curvature with trivial topology. We consider such a notion from the viewpoint of optimal transport which gives a natural distance structure between probability measures. This allows us to uniquely interpolate many probability distributions, called the Wasserstein barycentre, as initiated by Agueh and Carlier. It also leads to a uniquely defined canonical barycentre, which is obtained by relaxing the notion of barycentre point to a barycentre measure. We will explain these developments, based on join work with Brendan Pass
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