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September 2011 Geometry of the Poisson Boolean model on a region of logarithmic width in the plane
Amites Dasgupta, Rahul Roy, Anish Sarkar
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Adv. in Appl. Probab. 43(3): 616-635 (September 2011). DOI: 10.1239/aap/1316792662

Abstract

Consider the region L = {(x ,y) : 0 ≤ yClog(1 + x), x > 0} for a constant C > 0. We study the percolation and coverage properties of this region. For the coverage properties, we place a Poisson point process of intensity λ on the entire half space R+ x R and associated with each Poisson point we place a box of a random side length ρ. Depending on the tail behaviour of the random variable ρ we exhibit a phase transition in the intensity for the eventual coverage of the region L. For the percolation properties, we place a Poisson point process of intensity λ on the region R2. At each point of the process we centre a box of a random side length ρ. In the case ρ ≤ R for some fixed R > 0 we study the critical intensity λc of the percolation on L.

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Amites Dasgupta. Rahul Roy. Anish Sarkar. "Geometry of the Poisson Boolean model on a region of logarithmic width in the plane." Adv. in Appl. Probab. 43 (3) 616 - 635, September 2011. https://doi.org/10.1239/aap/1316792662

Information

Published: September 2011
First available in Project Euclid: 23 September 2011

zbMATH: 1227.60109
MathSciNet: MR2858213
Digital Object Identifier: 10.1239/aap/1316792662

Subjects:
Primary: 60D05, 60K35

Rights: Copyright © 2011 Applied Probability Trust

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Vol.43 • No. 3 • September 2011
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