TY - JOUR
T1 - Divergence for s-concave and log concave functions
AU - Caglar, Umut
AU - Werner, Elisabeth M.
PY - 2014/6/1
Y1 - 2014/6/1
N2 - We prove new entropy inequalities for log concave and s-concave functions that strengthen and generalize recently established reverse log Sobolev and Poincaré 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.
AB - We prove new entropy inequalities for log concave and s-concave functions that strengthen and generalize recently established reverse log Sobolev and Poincaré 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.
KW - Affine isoperimetric inequalities
KW - Divergence
KW - Entropy
KW - Log Sobolev inequalities
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U2 - 10.1016/j.aim.2014.02.013
DO - 10.1016/j.aim.2014.02.013
M3 - Article
AN - SCOPUS:84897713231
SN - 0001-8708
VL - 257
SP - 219
EP - 247
JO - Advances in Mathematics
JF - Advances in Mathematics
ER -