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


Mass transport


infinite clusters

Uniqueness in

Poisson Boolean model

Homogeneous spaces


Johan Tykesson

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics

Journal of Theoretical Probability

0894-9840 (ISSN) 1572-9230 (eISSN)

Vol. 22 2 402-417

Subject Categories

Probability Theory and Statistics



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