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Percolation of Poisson sticks on the plane. (English) Zbl 0725.60115
We consider a percolation model on the plane which consists of 1- dimensional sticks placed at points of a Poisson process on $${\mathbb{R}}^ 2$$; each stick having a random, but bounded length and a random direction. The critical probabilities are defined with respect to the occupied clusters and vacant clusters, and they are shown to be equal. The equality is shown through a ‘pivotal cell’ argument, using a version of the Russo-Seymour-Welsh theorem which we obtain for this model.
Reviewer: R.Roy (New Delhi)

##### MSC:
 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82B43 Percolation
##### Keywords:
percolation model; critical probabilities; clusters
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##### References:
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