Inner regularization of log-concave measures and small-ball estimates

Bo'Az Klartag*, Emanuel Milman

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

In the study of concentration properties of isotropic log-concave measures, it is often useful to first ensure that the measure has super-Gaussian marginals. To this end, a standard preprocessing step is to convolve with a Gaussian measure, but this has the disadvantage of destroying small-ball information. We propose an alternative preprocessing step for making the measure seem super-Gaussian, at least up to reasonably high moments, which does not suffer from this caveat: namely, convolving the measure with a random orthogonal image of itself. As an application of this "inner-thickening", we recover Paouris' small-ball estimates.

Original languageEnglish
Title of host publicationGeometric Aspects of Functional Analysis
Subtitle of host publicationIsrael Seminar 2006-2010
PublisherSpringer Verlag
Pages267-278
Number of pages12
ISBN (Print)9783642298486
DOIs
StatePublished - 2012

Publication series

NameLecture Notes in Mathematics
Volume2050
ISSN (Print)0075-8434

Funding

FundersFunder number
German Israeli Foundation’s Young Scientist ProgramI-2228-2040.6/2009
Taub Foundation
European Commission900/10
United States-Israel Binational Science Foundation2010288
Israel Science Foundation

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