PreprintCC BY-NC-ND 4.0HAL
Embedding large subsets of Wasserstein spaces into Banach spaces
Abstract
Embedding subsets of Wasserstein spaces into linear spaces is a problem of both theoretical and computational interest. In this work, we prove that three classical and natural embeddings of Wasserstein spaces into Banach spaces of non-trivial type are bi-Hölder on subsets of Wasserstein spaces given by moment bounds. These embeddings, all considered in multiple applications, are the linearized optimal transport embedding, the sliced-Wasserstein embedding, and a particular kernel mean embedding. Our results contrast with known obstructions to embeddin the full Wasserstein space into Banach spaces of non-trivial type. We also show the sharpness of our results regarding the moments required for our conclusions to hold.
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BibTeX
@misc{letrouit2026embedding,
title = {{Embedding large subsets of Wasserstein spaces into Banach spaces}},
author = {Cyril Letrouit and Quentin Merigot},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12029},
eprint = {2610.12029},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05788044v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Embedding large subsets of Wasserstein spaces into Banach spaces
AU - Cyril Letrouit
AU - Quentin Merigot
PY - 2026
DA - 2026/10/08
PB - HAL
DO - 10.48550/arxiv.2610.12029
UR - https://hal.science/hal-05788044v1
AB - Embedding subsets of Wasserstein spaces into linear spaces is a problem of both theoretical and computational interest. In this work, we prove that three classical and natural embeddings of Wasserstein spaces into Banach spaces of non-trivial type are bi-Hölder on subsets of Wasserstein spaces given by moment bounds. These embeddings, all considered in multiple applications, are the linearized optimal transport embedding, the sliced-Wasserstein embedding, and a particular kernel mean embedding. Our results contrast with known obstructions to embeddin the full Wasserstein space into Banach spaces of non-trivial type. We also show the sharpness of our results regarding the moments required for our conclusions to hold.
ER -