Mean Width of a Regular Cross-Polytope

Details Mean Width of a Regular Cross-Polytope Mean Width of a Regular Cross-Polytope

2011-12-02

arxiv.org/abs/1112.0499v1

Mathematics

Metric Geometry

11 pages

Scientific paper

The expected range of a sample of n+1 normally distributed variables is known to be related to the mean width of a regular n-simplex. We show that the expected maximum mu_n of a sample of n half-normally distributed variables is related to the mean width of a regular n-crosspolytope. Both of these relations have mean square counterparts. An expression for mu_5 is found and is believed to be new.

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