Percolation of Poisson sticks on the plane

Roy, Rahul (1991) Percolation of Poisson sticks on the plane Probability Theory and Related Fields, 89 (4). pp. 503-517. ISSN 0178-8051

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We consider a percolation model on the plane which consists of 1-dimensional sticks placed at points of a Poisson process on R2; 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.

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