A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is
Let be a sequence of independent and identically distributed random vectors drawn from the d-dimensional unit ball Bd and let Xn be the random polytope generated as the convex hull of a 1,· ··, an. Furthermore, let Δ(Xn ): = Vol (Bd Xn ) be the volume of the part of the ball lying outside the random polytope. For uniformly distributed ai and 2 we prove that the limiting distribution of Δ(Xn )/Ε (Δ (Xn )) for n → ∞ (satisfies a 0–1 law. In particular, we show that Var for n → ∞. We providedoi:10.2307/1427895 fatcat:a6dm2vj7e5a4vhhzq75mu7tylu