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On the closure under barycenters of location-scatter families with a normalized generator
Pietro Aldrigo
Source abstract
We provide an example of a normalized absolutely continuous probability whose location-scatter family (LSF) does not contain all the 2-Wassertein geodesics passing through its elements. In particular, we find a counterexample for Corollary 4.5 in [2]. Finally, we prove that LSFs with a (possibly singular) radially symmetric generator are closed under 2-Wasserstein barycenters.
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