The Russo-Seymour-Welsh Theorem and the Equality of Critical Densities and the "Dual" Critical Densities for Continuum Percolation on $|mathbb{R}^2$
Roy, Rahul
Ann. Probab., Tome 18 (1990) no. 4, p. 1563-1575 / Harvested from Project Euclid
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A Russo-Seymour-Welsh (RSW) theorem is established for continuum percolation on $\mathbb{R}^2$. The equality of various definitions of critical densities for the continuum percolation on $\mathbb{R}^2$ is deduced as an application of the RSW theorem. It is also shown that various notions of the size of a cluster yield the same notion of critical density.
Publié le : 1990-10-14
Classification:  Poisson process,  continuum percolation,  critical densities,  FKG inequality,  RSW theorem,  60K35,  82A43,  82A68,  60K10 
@article{1176990632,
     author = {Roy, Rahul},
     title = {The Russo-Seymour-Welsh Theorem and the Equality of Critical Densities and the "Dual" Critical Densities for Continuum Percolation on $|mathbb{R}^2$},
     journal = {Ann. Probab.},
     volume = {18},
     number = {4},
     year = {1990},
     pages = { 1563-1575},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176990632}
}

Roy, Rahul. The Russo-Seymour-Welsh Theorem and the Equality of Critical Densities and the "Dual" Critical Densities for Continuum Percolation on $|mathbb{R}^2$. Ann. Probab., Tome 18 (1990) no. 4, pp.  1563-1575. http://gdmltest.u-ga.fr/item/1176990632/