Wasserstein barycenter convexity of entropy characterizes Hilbert spaces among finite-dimensional normed spaces.
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math.MG 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Establishes an explicit strong-convexity modulus for the barycentric variance functional on Alexandrov spaces, implying Hölder stability of barycenters and empirical consistency bounds without using linear structure.
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Wasserstein Barycenter Convexity Detects Hilbertian Geometry
Wasserstein barycenter convexity of entropy characterizes Hilbert spaces among finite-dimensional normed spaces.
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Quantitative Stability of Wasserstein Barycenters over Alexandrov Spaces with Lower Curvature Bounds
Establishes an explicit strong-convexity modulus for the barycentric variance functional on Alexandrov spaces, implying Hölder stability of barycenters and empirical consistency bounds without using linear structure.