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- W4230223904 abstract "Consider the region L = {( x , y ): 0 ≤ y ≤ C log(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 R 2 . 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 λ c of the percolation on L ." @default.
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- W4230223904 date "2011-09-01" @default.
- W4230223904 modified "2023-10-16" @default.
- W4230223904 title "Geometry of the Poisson Boolean model on a region of logarithmic width in the plane" @default.
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- W4230223904 doi "https://doi.org/10.1017/s0001867800005061" @default.
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