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Gromov-Hausdorff convergence of discrete optimal transport Maas, Jan


For a natural class of discretisations of a convex domain in $R^n$, we consider the dynamical optimal transport metric for probability measures on the discrete mesh. Although the associated discrete heat flow converges to the continuous heat flow, we show that the transport metric may fail to converge to the 2-Kantorovich metric. Under an additional symmetry condition on the mesh, we show that Gromov-Hausdorff convergence to the 2-Kantorovich metric holds. This is joint work with Peter Gladbach and Eva Kopfer.

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