Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Letrouit, Cyril, Mérigot, Quentin
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221196149