From survival to extinction of the contact process by the removal of a single edge. (English) Zbl 1348.82058

Summary: We give a construction of a tree in which the contact process with any positive infection rate survives but, if a certain privileged edge \(e^*\) is removed, one obtains two subtrees in which the contact process with infection rate smaller than \(1/4\) dies out.


82C22 Interacting particle systems in time-dependent statistical mechanics
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