Open AccessInequalities for generalized entropy and optimal transportation
Author(s) -
Dario Cordero–Erausquin,
Wilfrid Gangbo,
Christian Houdré
Publication year - 2004
Publication title -
contemporary mathematics - american mathematical society
Language(s) - English
Resource type - Reports
SCImago Journal Rank - 0.106
H-Index - 12
eISSN - 1098-3627
pISSN - 0271-4132
DOI - 10.1090/conm/353/06433
Subject(s) - mathematics , inequality , entropy (arrow of time) , pure mathematics , mathematical analysis , thermodynamics , physics
A new concept of Fisher-information is introduced through a cost function. That concept is used to obtain extensions and variants of transport and logarithmic Sobolev inequalities for general entropy functionals and transport costs. Our proofs rely on optimal mass transport from the Monge-Kantorovich theory. They express the convexity of entropy functionals with respect to suitably chosen paths on the set of probability measures.
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