Description
A random beta-prime polytope is the convex hull of i.i.d. random points selected according to beta-prime distributions in /d/-dimensional Euclidean space. After a suitable rescaling, beta-prime polytopes converge in distribution to the convex hulls of Poisson point processes with power-law intensity density functions. We prove convergence of moments for the intrinsic volumes of random beta-prime polytopes.
We also consider a spherical model, in which the random points are chosen from the /d-/dimensional upper open half-sphere. The spherical convex hull of the random points is a spherical random polytope. After gnomonic projection, the push-forwards of such polytopes are beta-prime polytopes. We prove moment convergence of the spherical volume of the spherical random polytopes.
This is joint work with F. Fodor and P. Kevei (University of Szeged, Hungary).
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