Multi-distribution Rényi divergences are positive integrals of coincidence divergences C_α over four strata (simplex interior, mixed-sign cones, tropical boundary, KL edges).
Barycentric decompositions for extensive monotone divergences
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Sufficient and almost necessary conditions for large-sample and catalytic majorization of finite statistical experiments on Borel spaces are characterized by inequalities on multivariate Renyi divergences.
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Multi-distribution Rényi divergences are positive integrals of coincidence divergences C_α over four strata (simplex interior, mixed-sign cones, tropical boundary, KL edges).
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Multivariate majorization of continuous statistical experiments
Sufficient and almost necessary conditions for large-sample and catalytic majorization of finite statistical experiments on Borel spaces are characterized by inequalities on multivariate Renyi divergences.