Poisson – Voronoi Approximation
نویسنده
چکیده
Let X be a Poisson point process and K ⊂ R d a measurable set. Construct the Voronoi cells of all points x ∈ X with respect to X, and denote by vX (K) the union of all Voronoi cells with nucleus in K. For K a compact convex set the expectation of the volume difference V (vX (K)) − V (K) and the symmetric difference V (vX (K)△K) is computed. Precise estimates for the variance of both quantities are obtained which follow from a new jackknife inequality for the variance of functionals of a Poisson point process. Concentration inequalities for both quantities are proved using Azuma's inequality.
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