High-dimensional star-shaped distributions

Geometric disintegration and star-shaped distributions

Geometric and stochastic representations are derived for the big class of p-generalized elliptically contoured distributions, and (generalizing Cavalieri?s and Torricelli?s method of indivisibles in a non-Euclidean sense) a geometric disintegration method is established for deriving even more general star-shaped distributions. Applications to constructing non-concentric elliptically contoured a...

Convex and star-shaped sets associated with stable distributions

It is known that each symmetric stable distribution in Rd is related to a norm on Rd that makes Rd embeddable in Lp([0, 1]). In case of a multivariate Cauchy distribution the unit ball in this norm corresponds is the polar set to a convex set in Rd called a zonoid. This work exploits most recent advances in convex geometry in order to come up with new probabilistic results for multivariate stab...

Global Existence for High Dimensional Quasilinear Wave Equations Exterior to Star-shaped Obstacles

1. Introduction. The purpose of this article is to study long time existence for high dimensional quasilinear wave equations exterior to star-shaped obstacles. In particular, we seek to prove exterior domain analogs of the four dimensional results of [5] where the nonlinearity is permitted to depend on the solution not just its first and second derivatives. Previous proofs in exterior domains o...

Star-Shaped and L-Shaped Orthogonal Drawings

An orthogonal drawing of a plane graph G is a planar drawing of G, denoted by D(G), such that each vertex of G is drawn as a point on the plane, and each edge of G is drawn as a sequence of horizontal and vertical line segments with no crossings. An orthogonal polygon P is called orthogonally convex if the intersection of any horizontal or vertical line L and P is either a single line segment o...

Convexifying star-shaped polygons