# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## On the infimum convolution inequality

### Tom 189 / 2008

Studia Mathematica 189 (2008), 147-187 MSC: Primary 52A20; Secondary 52A40, 60E15. DOI: 10.4064/sm189-2-5

#### Streszczenie

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 ${\rm IC}$ inequalities are tied to concentration and study the optimal cost functions for an arbitrary probability measure $\mu$. In particular, we prove an optimal ${\rm IC}$ inequality for product log-concave measures and for uniform measures on the $\ell_p^n$ balls. Such an optimal inequality implies, for a given measure, the central limit theorem of Klartag and the tail estimates of Paouris.

#### Autorzy

• R. LatałaInstitute of Mathematics
University of Warsaw
Banacha 2
02-097 Warszawa, Poland
and
Institute of Mathematics
P.O. Box 21
00-956 Warszawa 10, Poland
e-mail
• J. O. WojtaszczykInstitute of Mathematics
University of Warsaw
Banacha 2
02-097 Warszawa, Poland
e-mail

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