Abstract
We consider two independent homogeneous Poisson processes Π0and Π1in the plane with intensities λ0and λ1, respectively. We study additive functionals of the set of Π0-particles within a typical Voronoi Π1-cell. We find the first and the second moments of these variables as well as upper and lower bounds on their distribution functions, implying an exponential asymptotic behavior of their tails. Explicit formulae are given for the number and the sum of distances from Π0-particles to the nucleus within a typical Voronoi Π1-cell.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
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