Pinsker inequalities and related Monge-Amp\`ere equations for log concave functions

Autor:	Caglar, Umut, Kolesnikov, Alexander V., Werner, Elisabeth M.
Rok vydání:	2020
Předmět:	Mathematics - Differential Geometry Mathematics - Metric Geometry
Druh dokumentu:	Working Paper
Popis:	In this paper we further develop the theory of f-divergences for log-concave functions and their related inequalities. We establish Pinsker inequalities and new affine invariant entropy inequalities. We obtain new inequalities on functional affine surface area and lower and upper bounds for the Kullback-Leibler divergence in terms of functional affine surface area. The functional inequalities lead to new inequalities for L_p-affine surface areas for convex bodies.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2005.07055 Zobrazit plný text záznamu View this record from Arxiv