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. © 2012 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Klartag, B., & Milman, E. (2012). Inner regularization of log-concave measures and small-ball estimates. Lecture Notes in Mathematics, 2050, 267–278. https://doi.org/10.1007/978-3-642-29849-3_15
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