Frankie Higgs

activity

20232025

collaborators

4 papers

math.PR2025

Exponential decay for the random connection model using asymptotic transitivity

Frankie Higgs

We prove that the probability the cluster of the origin in a subcritical Poisson random connection model (RCM) has size at least $n$ decays exponentially as $n$ increases, under mi…

math.PR2024

Random coverage from within with variable radii, and Johnson-Mehl cover times

Mathew D. Penrose, Frankie Higgs

Given a compact planar region $A$ , let $τ_{A}$ be the (random) time it takes for the Johnson-Mehl tessellation of $A$ to be complete, i.e. the time it takes for $A$ to be fully cover…

math.PR2024

Covering one point process with another

Frankie Higgs, Mathew D. Penrose, Xiaochuan Yang

Let $X_{1}, X_{2}, \dots$ and $Y_{1}, Y_{2}, \dots$ be i.i.d. random uniform points in a bounded domain $A \subset R^{2}$ with smooth or polygonal boundary. Given $n,m,k \in \math…

math.PR2023

Largest nearest-neighbour link and connectivity threshold in a polytopal random sample

Mathew D. Penrose, Xiaochuan Yang

Let $X_{1}, X_{2}, \dots$ be independent identically distributed random points in a convex polytopal domain $A \subset R^{d}$ . Define the largest nearest neighbour link $L_{n}$ t…