Author

John Fernley

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Preprint Sep 2026

Percolation of the contact process on the regular tree

The contact process on the regular tree $\mathbb{T}_d$ when $d\geq 3$ has the two phase transitions of global and of local survival, found by Pemantle and Liggett at values $\lambda_1$ and $\lambda_2$. We start the system with every vertex infected and let it relax to what is known as the upper invariant infection. In...

John Fernley, Emmanuel M. Jacob · 0 citations

Preprint Sep 2026

The voter model on the hyperbolic graph

We consider the voter model on the giant component of a hyperbolic random graph, which is a spatial scale-free network, in the sparse and linear-giant regime $\alpha\in(1/2,1)$. We find that the quenched expected consensus time has order $n^{2-1/\alpha}$, as the number of vertices $n\to\infty$, with probability arbitra...

John Fernley, Christian Hirsch · 0 citations