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On the infimum convolution inequality

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Latała R., Wojtaszczyk J.

Studia Mathematica

2008

tom 189

nr 2

147-187

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.

Ograniczanie wyników

1 Studia Mathematica

1 Latała R.

1 Wojtaszczyk J.

1 2008

Wyniki wyszukiwania

On the infimum convolution inequality