Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591895 | Journal of Functional Analysis | 2008 | 19 Pages |
Abstract
We prove a pointwise version of the multi-dimensional central limit theorem for convex bodies. Namely, let μ be an isotropic, log-concave probability measure on Rn. For a typical subspace E⊂Rn of dimension nc, consider the probability density of the projection of μ 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.
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