Renyi Entropy of Marginal distributions
Peter Harremoes and Christophe Vignat
Journal of Multivariate Analysis
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.