Old and new

By C. McBride, Catherine E. Snow, Natalia Kucirkova, V. Grøver. 2017

356 citations recorded by the source corpus.

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On Wasserstein Two-Sample Testing and Related Families of Nonparametric Tests (2015, background): “The theory of optimal transport (see [Villani, 2009]) provides a set of powerful tools to compare probability measures and distributions on Rd through the knowledge of a metric on Rd, which we assume to be the usual Euclidean metric in what follows.”
Non-Contraction of Heat Flow on Minkowski Spaces (2010, methodology): “We refer to [AGS] and [Vi] for Wasserstein geometry as well as the gradient flow theory.”
Bochner-Weitzenb\"ock formula and Li-Yau estimates on Finsler manifolds (2011, background): “A little knowledge of optimal transport theory is necessary for which we refer to [Vi] and [Oh1].”
Displacement convexity of generalized relative entropies (2010, background): “Recent astonishing development of optimal transport theory reveals that the displacement convexity of entropy-type functionals plays important roles in the theory of partial differential equations, probability theory and differential geometry (see [AGS], [Vi1], [Vi2] and the references therein).”