Continuum Percolation at and above the Uniqueness Threshold on Homogeneous Spaces
Journal article, 2009
We consider the Poisson Boolean model of continuum percolation on a homogeneous space M. Let lambda be the intensity of the underlying Poisson process. Let lambda (u) be the infimum of the set of intensities that a.s. produce a unique unbounded component. First we show that if lambda >lambda (u) , then there is a.s. a unique unbounded component at lambda. Then we let M=H(2)xR and show that at lambda (u) there is a.s. not a unique unbounded component. These results are continuum analogs of theorems by Haggstrom, Peres and Schonmann.
Continuum percolation
graphs
Mass transport
percolation
infinite clusters
Uniqueness in
Poisson Boolean model
Homogeneous spaces
Author
Johan Tykesson
University of Gothenburg
Chalmers, Mathematical Sciences, Mathematical Statistics
Journal of Theoretical Probability
0894-9840 (ISSN) 1572-9230 (eISSN)
Vol. 22 2 402-417Subject Categories
Probability Theory and Statistics
DOI
10.1007/s10959-008-0179-1