Abstract
We prove that the total variation distance between the cone measure and surface measure on the sphere of ℓ p n is bounded by a constant times 1/ √n. This is used to give a new proof of the fact that the coordinates of a random vector on the ℓ p n sphere are approximately independent with density proportional to exp(- t p ), a unification and generalization of two theorems of Diaconis and Freedman. Finally, we show in contrast that a projection of the surface measure of the ℓ p n sphere onto a random k-dimensional subspace is "close" to the k-dimensional Gaussian measure.
Original language | English (US) |
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Pages (from-to) | 241-261 |
Number of pages | 21 |
Journal | Annales de l'institut Henri Poincare (B) Probability and Statistics |
Volume | 39 |
Issue number | 2 |
DOIs | |
State | Published - 2003 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty