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The aim is to understand how the generalized Ricci tensor can be estimated in weighted Riemannian manifolds using Wasserstein distances.

Coarse Ricci curvature of weighted Riemannian manifolds

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The aim is to understand how the generalized Ricci tensor can be estimated in weighted Riemannian manifolds using Wasserstein distances.
Analyzed the generalized Ricci tensor in weighted complete Riemannian manifolds.
Utilized scaled metric derivatives of Wasserstein 1-distances.
Applied findings to random geometric graphs from Poisson point processes.
Demonstrated asymptotic retrieval of generalized Ricci tensor from metric derivatives.
Showed convergence of coarse curvature in graphs to the generalized Ricci tensor.

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Analysis reveals relationships between coarse curvature and generalized Ricci tensor in geometric graphs.

Arnaudon et al. (2025) studied this question.

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