An extension of the entropy power inequality to the form <inline-formula> <tex-math notation="LaTeX">$N_{r}^\alpha (X+Y) \geq N_{r}^\alpha (X) + N_{r}^\alpha (Y)$ </tex-math></inline-formula> withâ€¦ (More)

Elaborating on the similarity between the entropy power inequality and the Brunn-Minkowski inequality, Costa and Cover conjectured in On the similarity of the entropy power inequality and theâ€¦ (More)

Article history: Received 6 November 2015 Accepted after revision 11 December 2015 Available online 27 January 2016 Presented by Gilles Pisier Let us define, for a compact set A âŠ‚ Rn , the Minkowskiâ€¦ (More)

We derive a lower bound on the differential entropy of a log-concave random variable X in terms of the p-th absolute moment of X. The new bound leads to a reverse entropy power inequality with anâ€¦ (More)

We prove that a general class of measures, which includes logconcave measures, is 1 n -concave according to the terminology of Borell, with additional assumptions on the measures or on the sets, suchâ€¦ (More)

Let us define for a compact set A âŠ‚ R the sequence A(k) = { a1 + Â· Â· Â·+ ak k : a1, . . . , ak âˆˆ A } = 1 k ( A+ Â· Â· Â·+A } {{ } k times ) . It was independently proved by Shapley, Folkman and Starrâ€¦ (More)

In this paper we establish concavity properties of two extensions of the classical notion of the outer parallel volume. On the one hand, we replace the Lebesgue measure by more general measures. Onâ€¦ (More)

2018 IEEE International Symposium on Informationâ€¦

2018

Using a sharp version of the reverse Young inequality, and a Renyi entropy comparison result due to Fradelizi, Madiman, and Wang, the authors derive a Renyi entropy power inequality for log-concaveâ€¦ (More)