  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.
