On random graphs with degree distribution bounded below by θ+2 and all moments finite, the discrete-time threshold-θ contact process exhibits a discontinuous phase transition between exponential survival and logarithmic extinction.
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A discontinuous phase transition in the threshold-$\theta \geq 2$ contact process on random graphs
On random graphs with degree distribution bounded below by θ+2 and all moments finite, the discrete-time threshold-θ contact process exhibits a discontinuous phase transition between exponential survival and logarithmic extinction.