Abstract of a paper by Ronen Eldan and Boaz Klartag
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 The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0708.2513 or http://arXiv.org/abs/0708.2513 or by email in unzipped form by transmitting an empty message with subject line uget 0708.2513 or in gzipped form by using subject line get 0708.2513 to: math@arXiv.org.
participants (1)
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Dale Alspach