Matthew Dickson

collaborators

3 papers

math.PR2026

Decay of connection probability in high-dimensional continuum percolation

Matthew Dickson, Yucheng Liu

We study a percolation model on $R^{d}$ called the random connection model. For $d$ large, we use the lace expansion to prove that the critical two-point connection probabili…

math.PR2025

Mean-field behaviour of the random connection model on hyperbolic space

Matthew Dickson, Markus Heydenreich

We study the random connection model on hyperbolic space $H^{d}$ in dimension $d = 2, 3$ . Vertices of the spatial random graph are given as a Poisson point process with intensi…

math.PR2025

Non-Uniqueness Phase in Hyperbolic Marked Random Connection Models using the Spherical Transform

Matthew Dickson

A non-uniqueness phase for infinite clusters is proven for a class of marked random connection models on the $d$ -dimensional hyperbolic space, $H^{d}$ , in a high volume-sc…