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Survival of multidimensional contact process in random environments. (English) Zbl 0768.60094
Summary: We consider contact processes in dimension $$d\geq 2$$, with death rates identically one and random infection rates i.i.d distributed on the space. We show that the process may survive although the distribution $$\lambda$$ of the infection rate is such that the expectation of $$[\log(1+\lambda)]^{d-\varepsilon}$$ is as close to zero as one wishes.

##### MSC:
 60K35 Interacting random processes; statistical mechanics type models; percolation theory
##### Keywords:
contact processes; random infection
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##### References:
 [1] Holley R. and Liggett T.M. (1978).The survival of contact processes. Ann. Probab.,6, 198–206. · Zbl 0375.60111 [2] Klein A. (199?).Extinction of contact and percolation processes in a random environment. Preprint. · Zbl 0814.60098 [3] Liggett T.M. (1992).The survival of one-dimensional contact processes in random environments. Ann. Probab.,20, 696–723. · Zbl 0754.60126 [4] Toom A.L. (1968).A family of uniform nets of formal neurons. Soviet Math. Dokl.,9, 1338–1341. · Zbl 0186.51101
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