TY - RPRT
A1 - Küfer, Karl-Heinz
T1 - On the expected number of shadow vertices of the convex hull of random points
N2 - Let \(a_1,\dots,a_m\) be independent random points in \(\mathbb{R}^n\) that are independent and identically distributed spherically symmetrical in \(\mathbb{R}^n\). Moreover, let \(X\) be the random polytope generated as the convex hull of \(a_1,\dots,a_m\) and let \(L_k\) be an arbitrary \(k\)-dimensional
subspace of \(\mathbb{R}^n\) with \(2\le k\le n-1\). Let \(X_k\) be the orthogonal projection image of \(X\) in \(L_k\). We call those vertices of \(X\), whose projection images in \(L_k\) are vertices of \(X_k\)as well shadow vertices of \(X\) with respect to the subspace \(L_k\) . We derive a distribution independent sharp upper bound for the expected number of shadow vertices of \(X\) in \(L_k\).
T3 - Preprints (rote Reihe) des Fachbereich Mathematik - 282
Y1 - 1996
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5051
UR - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-50516
ER -