Invariant measures exist for perturbed continuum contact processes without the criticality condition, and local mortality peaks do not lead to extinction, characterized via the Feynman-Kac formula.
Simon, Functional Integration and Quantum Physics, Academic Press, NY, 1979
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Persistence in perturbed contact models in continuum
Invariant measures exist for perturbed continuum contact processes without the criticality condition, and local mortality peaks do not lead to extinction, characterized via the Feynman-Kac formula.