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arXiv · 2610.32446

On the closure under barycenters of location-scatter families with a normalized generator

Pietro Aldrigo
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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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Pietro Aldrigo. 2026-10-23. On the closure under barycenters of location-scatter families with a normalized generator. https://arxiv.org/abs/2610.32446

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