Divergence for s-concave and log concave functions

By Umut Caglar, Elisabeth M. Werner. 2013

46 citations recorded by the source corpus.

Abstract We prove new entropy inequalities for log concave and s-concave functions that strengthen and generalize recently established reverse log Sobolev and Poincare inequalities for such functions. This leads naturally to the concept of f-divergence and, in particular, relative entropy for s-concave and log concave functions. We establish their basic properties, among them the affine invariant valuation property. Applications are given in the theory of convex bodies.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/22a41308679cfa77f9407eec8becfb17807f7699

Citations in the corpus

• Functional Versions of Lp-Affine Surface Area and Entropy Inequalities (2014, unknown): “Generalizations of a different nature were given in [12] and [13].”