@inbook{45b847ae0e634bda8e39abfe9a41828c,
title = "Inner regularization of log-concave measures and small-ball estimates",
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.",
author = "Bo'az Klartag and Emanuel Milman",
note = "Funding Information: We thank Olivier Gu{\'e}don and Vitali Milman for discussions. Bo{\textquoteright}az Klartag was supported in part by the Israel Science Foundation and by a Marie Curie Reintegration Grant from the Commission of the European Communities. Emanuel Milman was supported by the Israel Science Foundation (grant no. 900/10), the German Israeli Foundation{\textquoteright}s Young Scientist Program (grant no. I-2228-2040.6/2009), the Binational Science Foundation (grant no. 2010288), and the Taub Foundation (Landau Fellow).",
year = "2012",
doi = "10.1007/978-3-642-29849-3_15",
language = "الإنجليزيّة",
isbn = "978-3-642-29848-6",
volume = "2050",
series = "Lecture Notes in Mathematics",
publisher = "Springer Verlag",
pages = "267--278",
editor = "B Klartag and S Mendelson and VD Milman",
booktitle = "Geometric Aspects of Functional Analysis, Lecture Notes in Mathematics",
address = "ألمانيا",
}