The Central Limit Problem for Random Vectors with Symmetries

Elizabeth S. Meckes () and Mark W. Meckes ()
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Elizabeth S. Meckes: Case Western Reserve University
Mark W. Meckes: Case Western Reserve University

Journal of Theoretical Probability, 2007, vol. 20, issue 4, 697-720

Abstract: Abstract Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are coordinatewise symmetric, uniform in a regular simplex, or spherically symmetric. Our proofs are based on Stein’s method of exchangeable pairs; as far as we know, this approach has not previously been used in convex geometry. The spherically symmetric case is treated by a variation of Stein’s method which is adapted for continuous symmetries.

Keywords: Central limit problem; Convex bodies; Stein’s method (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10959-007-0119-5

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