Necessary and sufficient conditions are given for convergence to a unique IPVT on proper pointed measured metric spaces, with proofs for higher-rank symmetric spaces and Diestel-Leader graphs showing parameter independence and distinguishable cells.
Mikhail Gromov.Metric Structures for Riemannian and Non-Riemannian Spaces
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DMW relaxes and lower-bounds GW by transporting distributions of sampled distance matrices, with finite-sample bounds depending on intrinsic dimension and sliced/multi-scale variants for computation.
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Convergence towards Ideal Poisson--Voronoi tessellations with a focus on Diestel--Leader graphs
Necessary and sufficient conditions are given for convergence to a unique IPVT on proper pointed measured metric spaces, with proofs for higher-rank symmetric spaces and Diestel-Leader graphs showing parameter independence and distinguishable cells.
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Distance-Matrix Wasserstein Statistics for Scalable Gromov--Wasserstein Learning
DMW relaxes and lower-bounds GW by transporting distributions of sampled distance matrices, with finite-sample bounds depending on intrinsic dimension and sliced/multi-scale variants for computation.