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Random spatial growth with paralyzing obstacles. (English) Zbl 1181.60151
The authors consider following model of spatial growth processes where initially there are sources of growth indicated by the colour green and sources of a growth-stopping (paralyzing) substance indicated by red. Let \(G\) be a connected, countably infinite graph of bounded degree. Each vertex of graph \(G\) is initially, independently of the other vertices, white (vacant), red or green with probabilities \(p_w, p_r\) and \(p_g\) respectively. Each edge of \(G\) is initially closed. It is proved that if the initial density of red vertices is positive, and that of white vertices is sufficiently small, the model is indeed well defined and the distribution has an exponential tail.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60K37 Processes in random environments
82B43 Percolation
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