This is an announcement for the paper "Pointwise estimates for marginals of convex bodies" by Ronen Eldan and Boaz Klartag.

Abstract: We prove a pointwise version of the multi-dimensional central limit theorem for convex bodies. Namely, let X be an isotropic random vector in R^n with a log-concave density. For a typical subspace E in R^n of dimension n^c, consider the probability density of the projection of X onto E. We show that the ratio between this probability density and the standard gaussian density in E is very close to 1 in large parts of E. Here c > 0 is a universal constant. This complements a recent result by the second named author, where the total-variation metric between the densities was considered.

Archive classification: math.MG math.FA

Remarks: 17 pages

The source file(s), pointwise.tex: 43054 bytes, is(are) stored in gzipped form as 0708.2513.gz with size 13kb. The corresponding postcript file has gzipped size 100kb.

Submitted from: bklartag@princeton.edu

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