×

Volumetric properties of the convex hull of an \(n\)-dimensional Brownian motion. (English) Zbl 1298.52005

The object of this paper is to study the convex hull \(K\) of the standard Brownian motion in \(\mathbb R^n\). The author extends some known results from the planar case to the higher dimensional case, as well as obtains certain asymptotics of the behaviour of these objects as the dimension goes to infinity. He introduces new methods which may be further used to study volumetric and combinatorial properties of the convex hull of the Brownian motion and random walk.

MSC:

52A22 Random convex sets and integral geometry (aspects of convex geometry)
60J65 Brownian motion
52A38 Length, area, volume and convex sets (aspects of convex geometry)
52A39 Mixed volumes and related topics in convex geometry
52C07 Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry)
PDFBibTeX XMLCite
Full Text: DOI arXiv