Betken, CarinaCarinaBetkenSchulte, MatthiasMatthiasSchulteThäle, ChristophChristophThäle2022-08-042022-08-042022-06Electronic Journal of Probability 27: 79, 1-47 (2022)http://hdl.handle.net/11420/13380This paper deals with the union set of a stationary Poisson process of cylinders in Rn having an (n − m)-dimensional base and an m-dimensional direction space, where m ∈ 0, 1, …, n − 1 and n ≥ 2. The concept simultaneously generalises those of a Boolean model and a Poisson hyperplane or m-flat process. Under very general conditions on the typical cylinder base a Berry-Esseen bound for the volume of the union set within a sequence of growing test sets is derived. Assuming convexity of the cylinder bases and of the window a similar result is shown for a broad class of geometric functionals, including the intrinsic volumes. In this context the asymptotic variance constant is analysed in detail, which in contrast to the Boolean model leads to a new degeneracy phenomenon. A quantitative central limit theory is developed in a multivariate set-up as well.en1083-64892022147Univ. of Washington, Mathematics Dep.https://creativecommons.org/licenses/by/4.0/Berry-Esseen boundcentral limit theoremgeometric functionalintrinsic volumemultivariate central limit theoremPoisson cylinder processsecond-order Poincaré inequalitystochastic geometryvariance asymptoticsTechnikJournal Article10.15480/882.453110.1214/22-EJP80510.15480/882.4531Journal Article