Year: 2013
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Caglar, Umut, Werner, Elisabeth M.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2949220935