M. Penrose

activity

20012026

most citedConnectivity of soft random geometric graphs

88 citations · 412 across the 47 of their papers we have counts for

collaborators

53 papers

math.PR2026

Record times for coverage thresholds and maximal spacings

Mathew D. Penrose

Let $X_{1}, X_{2}, \dots$ be independent uniform random points in a bounded region $A \subset R^{d}$ having a smooth boundary, $d \geq 1$ . Let $B \subset A$ be compact. The _cover…

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

Supercritical phase of the random connection model

Mathew D. Penrose

Given $d \in N, λ > 0$ , the random connection model (RCM) in a region $A \subseteq R^{d}$ is a graph with vertex set given by a homogeneous Poisson point process of intensi…

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

Largest component and sharpness in continuum percolation

Niclas Küpper, Mathew D. Penrose

We investigate the behavior of large connected components in the Poisson Random Connection model in non-critical regimes with any bounded connection function. We show that the asym…