Year: 2026
Type: preprint
Abstract: In [H. Lavenant, J. Luckhardt, G. Mordant, B. Schmitzer, L. Tamanini, The Riemannian geometry of Sinkhorn divergences. Ann. Inst. H. Poincaré Anal. Non Linéaire 43 (2026)] we introduced a Riemannian metric $\mathsf{d}_S$ on the space of probability distributions obtained from entropic optimal transport, specifically from the Sinkhorn divergence $S_\varepsilon$. In the present work we discuss how to approximate and compute $\mathsf{d}_S$. Spatially, we prove Gromov--Hausdorff convergence of the metric and convergence of geodesics for increasingly fine Eulerian discretization of the base space. Temporally, we show $Γ$-convergence of the chain discretization $N \sum_{k=0}^{N-1} S_\varepsilon(μ_k, μ_{k+1})$ to the energy functional defining $\mathsf{d}_S$. We deduce and implement numerical schemes to compute approximations of $\mathsf{d}_S$.
Source: arXiv (Cornell University)
Institutions: Bocconi University, University of Göttingen
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W7216086300