On the infimum convolution inequality

R. Latała, and J. O. Wojtaszczyk. "On the infimum convolution inequality." Studia Mathematica 189.2 (2008): 147-187. <http://eudml.org/doc/284942>.

@article{R2008,
abstract = {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.},
author = {R. Latała, J. O. Wojtaszczyk},
journal = {Studia Mathematica},
keywords = {infimum convolution; concetration; log-concave measure; isoperimetry;  ball},
language = {eng},
number = {2},
pages = {147-187},
title = {On the infimum convolution inequality},
url = {http://eudml.org/doc/284942},
volume = {189},
year = {2008},
}

TY - JOUR
AU - R. Latała
AU - J. O. Wojtaszczyk
TI - On the infimum convolution inequality
JO - Studia Mathematica
PY - 2008
VL - 189
IS - 2
SP - 147
EP - 187
AB - 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.
LA - eng
KW - infimum convolution; concetration; log-concave measure; isoperimetry;  ball
UR - http://eudml.org/doc/284942
ER -