This is an announcement for the paper "Inner regularization of log-concave measures and small-ball estimates" by Boaz Klartag and Emanuel Milman.

Authors: Bo'az Klartag and Emanuel Milman 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.

Archive classification: math.FA

Remarks: 12 pages

Submitted from: emanuel.milman@gmail.com

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1108.4856

or

http://arXiv.org/abs/1108.4856