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arXiv · 1307.5409

Divergence for s-concave and log concave functions

Umut Caglar·Elisabeth M. Werner
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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.

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Umut Caglar, Elisabeth M. Werner. 2013-07-20. Divergence for s-concave and log concave functions. https://arxiv.org/abs/1307.5409

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