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This paper presents asymptotic covariance formulae and central limit theoremsfor geometric functionals, including volume, surface area, and all Minkowskifunctionals and translation invariant Minkowski tensors as prominent examples,of stationary Boolean models. Special focus is put on the anisotropic case. Inthe (anisotropic) example of aligned rectangles, we provide explicit analyticformulae and compare them with simulation results. We discuss which informationabout the grain distribution second moments add to the mean values.

Second order analysis of geometric functionals of Boolean models