arXiv subjects
Publications and source records attributed to Richard A. Vitale.
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 a high dimensional setting), as well as a corresponding strong law of large numbers.
We discuss two research areas dealing respectively with (1) a class of multivariate medians and (2) a symmetrization algorithm for probability measures.
Extensions and variants are given for the well-known comparison principle for Gaussian processes based on ordering by pairwise distance.
Motivated from Gaussian processes, we derive the intrinsic volumes of the infinite--dimensional Brownian motion body. The method is by discretization to a class of orthoschemes. Numerical support is offered for a conjecture of Sangwine-Yager, and another conjecture is offered on the rate of decay of intrinsic volume sequences.