Kernel distances equal expected squared pairings with random fields, and a Gaussian free field version, the Dirichlet energy distance, extends the Cramer-von Mises distance to higher dimensions.
Sharp constants in the hardy-Littlewood-Sobolev and related inequalities
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Random Field Representations of Kernel Distances
Kernel distances equal expected squared pairings with random fields, and a Gaussian free field version, the Dirichlet energy distance, extends the Cramer-von Mises distance to higher dimensions.