Variance asymptotics and central limit theory for geometric functionals of Poisson cylinder processes

This paper deals with the union set of a stationary Poisson process cylinders in Rn having an (n−m)-dimensional base and m-dimensional direction space, where m∈{0,1,…,n−1} n≥2. The concept simultaneously generalises those Boolean model hyperplane or m-flat process. Under very general conditions on typical cylinder Berry-Esseen bound for volume within sequence growing test sets is derived. Assuming convexity bases window similar result shown broad class geometric functionals, including intrinsic volumes. In this context asymptotic variance constant analysed detail, which contrast to leads new degeneracy phenomenon. A quantitative central limit theory developed multivariate set-up as well.