A new framework defines channel cost and contraction via Lipschitz seminorms, proving duality, tensor properties, and applications to word length, Carnot-Carathéodory distance, and mixing times.
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Transportation cost and contraction coefficient for channels on von Neumann algebras
A new framework defines channel cost and contraction via Lipschitz seminorms, proving duality, tensor properties, and applications to word length, Carnot-Carathéodory distance, and mixing times.