Persistent survival of one-dimensional contact processes in random environments

Abstract

Consider an inhomogeneous contact process on Z 1 in which the recovery rates $\delta(x)$ at site x are i.i.d. random variables (bounded above) while the infection rate is a constant $\varepsilon$. The condition $u\mathbf{P}(-\log \varepsilon(x) > u) \to = \infty$ as $u \to = \infty$ implies the survival of the process for every $\varepsilon > 0$.