On the infimum convolution inequality

By Rafal Latala, Jakub Onufry Wojtaszczyk. 2008

89 citations recorded by the source corpus.

In the paper we study the infimum convolution inequalites. 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. In particular, we show the optimal IC-inequality for product log-concave measures and for uniform measures on the l_p^n balls. Such an optimal inequality implies, for a given measure, in particular the Central Limit Theorem of Klartag and the tail estimates of Paouris.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/cb02411ad04a9e65ac3aeb7980a1562ff019d4a7

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In Applied Mathematics

In Statistics and Probability

Citations in the corpus

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Robust covariance estimation under $L_{4}-L_{2}$ norm equivalence (2018, unknown): “, [4]) implies that ( E ∣∣∣∣ ∣∣∣∣ ∣∣∣∣ 1 N N ∑”
A generalization of Caffarelli’s contraction theorem via (reverse) heat flow (2010, unknown): “We refer to [38] for further examples of using contracting maps to transfer isoperimetric inequalities, and for further information.”
Relative entropy of cone measures and Lp centroid bodies (2009, background): “It was proved in [ 27 ] that Bp(K) is isomorphic to Zp(K),”
Transport Inequalities. A Survey (2010, methodology): “We refer to the works [95, 96] by Samson and [66] by Lata la and Wojtaszczyk for recent advances in the study of the Property (τ).”