All Questions

Suppose we choose $n$ uniformly random points in a disk, then draw the smallest circle that encloses all of those points. There is evidence suggesting that the probability that the enclosing circle is ...

Given a locally finite set of points $\{x_1,x_2,\dots\}\subset\mathbb{R}^d$, the Voronoi cell of a point $x_{i}$, denoted by $C(x_{i})$, consists of all the points in $\mathbb{R}^d$ that are closer to ...

Motivation: Let $\Gamma = (V,E)$ be a directed graph. To each edge $e \in E$, choose a value $\kappa^e \in \mathbb R$, representing the cost of transporting one unit of "stuff" through the edge. Let $\...

Say $\mathbb{R}^n$ is divided by $k>n$ randomly chosen hyperplanes. Each connected region away from the hyperplanes is the intersection of $k$ half-spaces, so it is a convex cone. It is known that ...

I know a number of (standard and well known) ways to measure the distance between two probability distributions and, more in general, to quantify how much one is far from another. Could you please ...