Divergence for s-concave and log concave functions

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.

References in corpus (2)

• Relative entropy of cone measures and $L_p$ centroid bodies
• Mixed $f$-divergence for multiple pairs of measures

Cited by in corpus (1)

• Functional versions of L_p-affine surface area and entropy inequalities