TY - RPRT
A1 - Küfer, Karl-Heinz
T1 - On the Approximation of a Ball by Random Polytopes
N2 - Let (\(a_i)_{i\in \bf{N}}\) be a sequence of identically and independently distributed random vectors drawn from the \(d\)-dimensional unit ball \(B^d\)and let \(X_n\):= convhull \((a_1,\dots,a_n\)) be the random polytope generated by \((a_1,\dots\,a_n)\). Furthermore, let \(\Delta (X_n)\) : = (Vol \(B^d\) \ \(X_n\)) be the deviation of the polytope's volume from the volume of the ball. For uniformly distributed \(a_i\) and \(d\ge2\), we prove that tbe limiting distribution of \(\frac{\Delta (X_n)} {E(\Delta (X_n))}\) for \(n\to\infty\) satisfies a 0-1-law. Especially, we provide precise information about the asymptotic behaviour of the variance of \(\Delta (X_n\)). We deliver analogous results for spherically symmetric distributions in \(B^d\) with regularly varying tail.
T3 - Preprints (rote Reihe) des Fachbereich Mathematik - 250
Y1 - 1994
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5050
UR - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-50509
ER -