×

Distributions of random simplices through Jacobians of matrix transformations. (English) Zbl 0976.60024

Stoka, Marius I. (ed.), Third international conference in stochastic geometry, convex bodies and empirical measures, Mazara del Vallo, Italy, May 24-29, 1999. Part I: Stochastic geometry. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 65, 219-232 (2000).
Author’s abstract: Consider an ordered set of \(p\) linearly independent random points in a Euclidean \(n\)-space, \(p\leq n + 1\). These \(p\) points almost surely determine a \(p\)-parallelotope. Arbitrary moments and the exact density of the content of this \(p\)-parallelotope will be examined without using any result from integral geometry. Some matrix transformations and the associated Jacobians will be used in the derivations. The situations considered are the cases when some of the \(p\) points are uniformly distributed over the surface of an \(n\)-sphere and the remaining points have some general distributions, uniform distribution being one among them.
For the entire collection see [Zbl 0955.00040].

MSC:

60D05 Geometric probability and stochastic geometry
52A22 Random convex sets and integral geometry (aspects of convex geometry)
53C65 Integral geometry
62H10 Multivariate distribution of statistics
PDFBibTeX XMLCite