English

Mean Width of a Regular Cross-Polytope

Metric Geometry 2016-03-15 v2 Probability

Abstract

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.

Cite

@article{arxiv.1112.0499,
  title  = {Mean Width of a Regular Cross-Polytope},
  author = {Steven R. Finch},
  journal= {arXiv preprint arXiv:1112.0499},
  year   = {2016}
}

Comments

11 pages

R2 v1 2026-06-21T19:45:21.439Z