2020/05/03 by Kabluchko, Zakhar, Thäle, Christoph
#52B11 #60D05 #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #Primary 52A22 #Probability (math.PR) #Secondary 52A55
paper · doi:10.48550/arxiv.2005.01055
The concept of typical and weighted typical spherical faces for tessellations of the d-dimensional unit sphere, generated by n independent random great hyperspheres distributed according to a non-degenerate directional distribution, is introduced and studied. Probabilistic interpretations for such spherical faces are given and their directional distributions are determined. Explicit formulas for the expected f-vector, the expected spherical Quermaßintegrals and the expected spherical intrinsic volumes are found in the isotropic case. Their limiting behaviour as n→∞ is discussed and compared to the corresponding notions and results in the Euclidean case. The expected statistical dimension and a problem related to intersection probabilities of spherical random polytopes is investigated.