Motivated from Gaussian processes, we derive the intrinsic volumes of the infiniteâ€“dimensional Brownian motion body. The method is by discretization to a class of orthoschemes. Numerical support isâ€¦ (More)

The Wills functional from the theory of lattice point enumeration can be adapted to produce the following exponential inequality for zero mean Gaussian processes: Ee sup t (X t ?(1=2) 2 t) e E sup tâ€¦ (More)

We provide a streamlined proof and improved estimates for the weak multivariate Gnedenko law of large numbers on concentration of random polytopes within the space of convex bodies (in a fixed or aâ€¦ (More)

Doubly stochastic measures can be identi ed with the trace of a pair of (Lebesgue) measure preserving maps of the unit interval to itself. It has been of traditional interest in probability theory toâ€¦ (More)

Intrinsic Lp metrics are defined and shown to satisfy a dimensionâ€“free bound with respect to the Hausdorff metric. MSC 2000: 52A20, 52A27, 52A40, 60G15.

Geometric and stochastic ideas interact in a wide variety of ways over both theory and applications. For two connections that do not seem to have been mentioned before, we present here descriptiveâ€¦ (More)

The package of APL routines described here grew out of some work pursued by the first author in the applications of convex geometry to pattern analysis of plane figures. In using these routines, ourâ€¦ (More)