Probabilistic frames and Wasserstein distances

2025/01/05 by Chen, Dongwei, Schmoll, Martin · 1 citation
#42C15 #49Q22 #60A10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2501.02602

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.

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