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Improved upper bounds for the contact process critical value. (English) Zbl 0832.60093
The basic one-dimensional contact process is a typical interacting particle system. It exhibits the phase transitions with critical value $$\lambda_c$$. The precise value $$\lambda_c$$ remains unknown up to now. The best known bounds are $$1.539 < \lambda_c < 2$$. The upper bound is due to R. Holley and the author [Ann. Probab. 6, 198-206 (1978; Zbl 0375.60111)]. The original proof is based on a renewal measure. The author develops a new technique. That is, using some perturbations of the measure instead of the original one. This needs a careful design and a lot of computations. In any case, the author is able to produce a new upper bound 1.942 by hand computation.

##### MSC:
 60K35 Interacting random processes; statistical mechanics type models; percolation theory
##### Keywords:
contact process; phase transitions; critical value; upper bound
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