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The Central Limit Problem for Random Vectors with Symmetries

Author

Listed:
  • Elizabeth S. Meckes

    (Case Western Reserve University)

  • Mark W. Meckes

    (Case Western Reserve University)

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.

Suggested Citation

  • Elizabeth S. Meckes & Mark W. Meckes, 2007. "The Central Limit Problem for Random Vectors with Symmetries," Journal of Theoretical Probability, Springer, vol. 20(4), pages 697-720, December.
    • Handle: RePEc:spr:jotpro:v:20:y:2007:i:4:d:10.1007_s10959-007-0119-5
    DOI: 10.1007/s10959-007-0119-5
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