Renyi Entropy of Marginal distributions
Peter Harremoes and Christophe Vignat
Journal of Multivariate Analysis 2006. ISSN 0047-259X

Abstract

In this paper we are interested in the n-dimensional uniform distributions on the sphere. We show that the marginal distribution maximizes the Renyi entropy under a moment constraint. Moreover, using an example we show that a distribution on a triangle with (uniform) maximum entropy marginals may have arbitrarily small entropy. As a last result we address the asymptotic behavior and make a link to the de Finetti Theorem.

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