Xiaochuan Yang

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20222025

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Showing 2024 · math.PRShow all

2 papers · 2 filters

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…