Cones generated by random points on half-spheres and convex hulls of Poisson point processes

Let U 1 , U 2 , … be random points sampled uniformly and independently from the d -dimensional upper half-sphere. We show that, as n → ∞ , the f -vector of the ( d + 1 ) -dimensional convex cone C n generated by U 1 , … , U n weakly converges to a certain limiting random vector, without any normaliz...

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