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Geometric properties of $N$ random points distributed independently and uniformly on the unit sphere $\mathbb{S}^{d}\subset\mathbb{R}^{d+1}$ with respect to surface area measure are obtained and several related conjectures are posed.
Über die Euler
E. Steinitz · 1906
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The m-distribution, a general formula of intensity of rapid fading
M. Nakagami · 1960
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A problem in geometric probability
J. G. Wendel · 1962
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Spherical Harmonics
C. Müller · 1966
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A synopsis of “Poisson flats in Euclidean spaces”
R. E. Miles · 1970
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Isotropic random simplices
R. E. Miles · 1971
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Covering the circle with random arcs
L. A. Shepp · 1972
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Stochastical approximation of convex bodies
C. Buchta, J. Müller, and R. F. Tichy · 1985
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A threshold for the size of random caps to cover a sphere
H. Maehara · 1988
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Random tessellations in 𝐑 d {\bf R}^{d}
J. Møller · 1989
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The next-order term for optimal Riesz and logarithmic energy asymptotics on the sphere
J. S. Brauchart, D. P. Hardin, and E. B. Saff · 2012
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Large convex holes in random point sets
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Intrinsic volumes of random polytopes with vertices on the boundary of a convex body
K. J. Böröczky, F. Fodor, and D. Hug · 2013
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Distributions of angles in random packing on spheres
T. Cai, J. Fan, and T. Jiang · 2013
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Extreme values for characteristic radii of a Poisson-Voronoi tessellation
P. Calka and N. Chenavier · 2014
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http://dlmf.nist.gov/, Release 1.0.9 of 2014-08-29
NIST Digital Library of Mathematical Functions · 2014
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NIST Handbook of Mathematical Functions
F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, editors · 2010
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