Xiaochuan Yang

collaborators

Showing math.PRShow all

5 papers · 1 filter

math.PR2025

Random coverage of a manifold with boundary

Mathew D. Penrose, Xiaochuan Yang

Let $A$ be a compact $d$ -dimensional $C^{2}$ Riemannian manifold with boundary, embedded in $R^{m}$ where $m \geq d \geq 2$ , and let $B$ be a nice subset of $A$ (possibly $B = A$ ).…

math.PR2025

Coverage of the unit cube by dynamic Boolean models

Hanna Döring, Lianne de Jonge, Xiaochuan Yang

Motivated by peer-to-peer telecommunication, we study a dynamic Boolean model. We define a Poisson number of random lines through the $(d - 1)$ -dimensional base of a $d$ -dimensional…

math.PR2025

On the components of random geometric graphs in the dense limit

Mathew D. Penrose, Xiaochuan Yang

Consider the geometric graph on $n$ independent uniform random points in a connected compact region $A$ of $R^{d}, d \geq 2$ , with $C^{2}$ boundary, or in the unit square, with d…

math.PR2024

Fluctuations of the connectivity threshold and largest nearest-neighbour link

Mathew D. Penrose, Xiaochuan Yang

Consider a random uniform sample of $n$ points in a compact region $A$ of Euclidean $d$ -space, $d \geq 2$ , with a smooth or (when $d = 2$ ) polygonal boundary. Fix $k \in N$ . Le…

math.PR2024

On the rate of convergence in the Hall-Janson coverage theorem

Mathew D. Penrose, Xiaochuan Yang

Consider a spherical Poisson Boolean model $Z$ in Euclidean $d$ -space with $d \geq 2$ , with Poisson intensity $t$ and radii distributed like $r Y$ with $r \geq 0$ a scaling paramete…