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Mean Width of a Regular Simplex

Metric Geometry 2016-03-15 v2 Probability

Abstract

The mean width is a measure on n-dimensional convex bodies. An integral formula for the mean width of a regular n-simplex appeared in the electrical engineering literature in 1997. As a consequence, expressions for the expected range of a sample of n+1 normally distributed variables, for n<=6, carry over to widths of regular n-simplices. As another consequence, precise asymptotics for the mean width become available as n->infty.

Cite

@article{arxiv.1111.4976,
  title  = {Mean Width of a Regular Simplex},
  author = {Steven R. Finch},
  journal= {arXiv preprint arXiv:1111.4976},
  year   = {2016}
}

Comments

12 pages

R2 v1 2026-06-21T19:39:22.452Z