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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 $λ_1$ and $λ_2$. We start the system with every vertex infected and let it relax to what is known as the upper invariant infect
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