Geometry of the Poisson Boolean model on a region of logarithmic width in the plane

Dasgupta, Amites ; Roy, Rahul ; Sarkar, Anish (2011) Geometry of the Poisson Boolean model on a region of logarithmic width in the plane Advances in Applied Probability, 43 (3). pp. 616-635. ISSN 0001-8678

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Official URL: http://projecteuclid.org/euclid.aap/1316792662

Related URL: http://dx.doi.org/10.1239/aap/1316792662

Abstract

Consider the region L = {(x ,y) : 0 ≤ y ≤ Clog(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+ × 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.

Item Type:Article
Source:Copyright of this article belongs to Applied Probability Trust.
Keywords:Boolean Model; Poisson Point Process; Percolation; Coverage
ID Code:72336
Deposited On:29 Nov 2011 13:40
Last Modified:29 Nov 2011 13:40

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