A Berry-Esseen type inequality for convex bodies with an unconditional basis

Details A Berry-Esseen type inequality for convex bodies with an unconditional basis A Berry-Esseen type inequality for convex bodies with an unconditional basis

2007-05-07

arxiv.org/abs/0705.0832v3

Mathematics

Probability

34 pages, minor revision: Some remarks and explanations were added. To appear in Probab. Theory Related Fields

Scientific paper

We provide a sharp rate of convergence in the central limit theorem for
random vectors with an unconditional, log-concave density. The argument relies
on analysis of the Neumann laplacian on convex domains and on the theory of
optimal transportation of measures.

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