Probabilistic frames and Wasserstein distances
Probability
2025-06-18 v2 Classical Analysis and ODEs
Abstract
We use Wasserstein distances to characterize and study probabilistic frames. Adapting results from Olkin and Pukelsheim, from Gelbrich and from Cuesta-Albertos, Matran-Bea and Tuero-Diaz to frame operators, we show that the sets of probabilistic frames with given frame operator are homeomorphic by an optimal linear push-forward. Using the Wasserstein distances, we generalize several recent results in probabilistic frame theory and show path connectedness of the set of probabilistic frames with a fixed frame operator. We also describe transport duals that do not arise as push-forwards and characterize those that are push-forwards.
Cite
@article{arxiv.2501.02602,
title = {Probabilistic frames and Wasserstein distances},
author = {Dongwei Chen and Martin Schmoll},
journal= {arXiv preprint arXiv:2501.02602},
year = {2025}
}