Research demonstrates contact process extinction in long-range interactions, suggesting critical transmission thresholds are vital.
We study the contact process on the long‐range percolation cluster on where each edge is open with probability for . Using a renormalization procedure, we apply the Peierls‐type argument to prove that the contact process dies out if the transmission rate is lower than a critical threshold. Our methods involve the control of crossing probabilities for percolation on randomly‐stretched lattices as in Hilário et al.
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Gomes et al. (2026) studied this question.
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