2023/03/03 by Hugo Leblanc, Thibaut Le Gouic, Leblanc, Hugo +5 · 1 citation
Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #Analysis of PDEs (math.AP) #Applied mathematics #Computer science #Dual (grammatical number) #FOS: Mathematics #Flow (mathematics) #Geometric Analysis and Curvature Flows #Geometry #Injective metric space #Intrinsic metric #Mathematical analysis #Mathematics #Metric (unit) #Metric Geometry (math.MG) #Metric space #Point processes and geometric inequalities #Probability (math.PR) #Probability measure #Pure mathematics #Set (abstract data type) #Space (punctuation) #Stein's method #Wasserstein metric
paper · pdf · doi:10.48550/arxiv.2303.02183
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2023/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define a metric in the space of positive finite positive measures that extends the 2-Wasserstein metric, i.e. its restriction to the set of probability measures is the 2-Wasserstein metric. We prove a dual and a dynamic formulation and extend the gradient flow machinery of the Wasserstein space. In addition, we relate the barycenter in this space to the barycenter in the Wasserstein space of the normalized measures.