The central limit problem for random vectors with symmetries

Details The central limit problem for random vectors with symmetries The central limit problem for random vectors with symmetries

2005-05-27

arxiv.org/abs/math/0505618v3

J. Theoret. Probab. 20 (2007), 697-720

Mathematics

Probability

AMS-LaTeX, uses xy-pic, 23 pages; v3: added new corollary to Theorem 7

Scientific paper

10.1007/s10959-007-0119-5

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 and we give a brief introduction to the classical method. The spherically symmetric case is treated by a variation of Stein's method which is adapted for continuous symmetries.

Affiliated with

Also associated with

No associations

Rating

The central limit problem for random vectors with symmetries does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The central limit problem for random vectors with symmetries, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The central limit problem for random vectors with symmetries will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-80338