Ferenc Fodor: Random ball-polytopes in balls and other smooth convex bodies

Abstract: We investigate the properties of uniform random ball-polytopes in
smooth convex bodies, and in particular, in the unit ball. We prove asymptotic
formulas for the expected number of proper facets of uniform random
ball-polytopes and point out some surprising phenomena in the unit ball,
namely, that the expected number of facets approaches a constant as the number
of random points tends to infinity.