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Entropy of spherical marginals and related inequalities

Abstract : We investigate relations between the entropy of a spherical density and those of its marginals, together with spherical convolution type inequalities. We extend results by Carlen, Lieb and Loss to more general configurations. Our argument involves a corresponding superadditivity result for Fisher information, which has a clear geometric meaning. (C) 2006 Elsevier SAS. All rights reserved.
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F. Barthe, Dario Cordero-Erausquin, B. Maurey. Entropy of spherical marginals and related inequalities. Journal de Mathématiques Pures et Appliquées, Elsevier, 2006, 86 (2), pp.89--99. ⟨10.1016/j.matpur.2006.04.003⟩. ⟨hal-00693099⟩



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