On the infimum convolution inequality

• Autorzy: R. Latała , J. O. Wojtaszczyk
• Języki publikacji: EN

Abstrakty

EN

We study the infimum convolution inequalities. Such an inequality was first introduced by B. Maurey to give the optimal concentration of measure behaviour for the product exponential measure. We show how IC inequalities are tied to concentration and study the optimal cost functions for an arbitrary probability measure μ. In particular, we prove an optimal IC inequality for product log-concave measures and for uniform measures on the $ℓⁿ_{p}$ balls. Such an optimal inequality implies, for a given measure, the central limit theorem of Klartag and the tail estimates of Paouris.

Kategorie tematyczne

• 60E15: Inequalities; stochastic orderings
• 52A40: Inequalities and extremum problems
• 52A20: Convex sets in n dimensions (including convex hypersurfaces)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 189
• Numer: 2
• Strony: 147-187

Daty

wydano

2008

Twórcy

autor

R. Latała

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 21, 00-956 Warszawa 10, Poland

autor

J. O. Wojtaszczyk

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/sm189-2-5