Divergence for s-concave and log concave functions
Functional Analysis
2013-07-23 v1
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.
Cite
@article{arxiv.1307.5409,
title = {Divergence for s-concave and log concave functions},
author = {Umut Caglar and Elisabeth M. Werner},
journal= {arXiv preprint arXiv:1307.5409},
year = {2013}
}