PreprintarXiv licencearXiv
On the closure under barycenters of location-scatter families with a normalized generator
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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BibTeX
@misc{aldrigo2026closure,
title = {{On the closure under barycenters of location-scatter families with a normalized generator}},
author = {Pietro Aldrigo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32446},
eprint = {2610.32446},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32446},
}
RIS
TY - UNPB
TI - On the closure under barycenters of location-scatter families with a normalized generator
AU - Pietro Aldrigo
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32446
UR - https://arxiv.org/abs/2610.32446
AB - 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.
ER -