an:04197125
Zbl 0725.60115
Roy, Rahul
Percolation of Poisson sticks on the plane
EN
Probab. Theory Relat. Fields 89, No. 4, 503-517 (1991).
00176554
1991
j
60K35 82B43
percolation model; critical probabilities; clusters
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.
R.Roy (New Delhi)