Random Polytopes in Smooth Convex Bodies
نویسندگان
چکیده
Let K<= R be a convex body and choose points xl,x2 xn randomly, independently, and uniformly from K. Then Kn = conv {x, , . . . , *„} is a random polytope that approximates K (as n -») with high probability. Answering a question of Rolf Schneider we determine, up to first order precision, the expectation of vol K -vol Kn when K is a smooth convex body. Moreover, this result is extended to quermassintegrals (instead of volume). §
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تاریخ انتشار 2009