Divergence for s-concave and log concave functions Article

Caglar, U, Werner, EM. (2014). Divergence for s-concave and log concave functions . ADVANCES IN MATHEMATICS, 257 219-247. 10.1016/j.aim.2014.02.013

cited authors

  • Caglar, U; Werner, EM

authors

abstract

  • We prove new entropy inequalities for log concave and s-concave functions that strengthen and generalize recently established reverse log Sobolev and Poincar√© 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. ¬© 2014 Elsevier Inc.

publication date

  • June 1, 2014

published in

Digital Object Identifier (DOI)

start page

  • 219

end page

  • 247

volume

  • 257