Lothar Heinrich

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The paper introduces a family of stationary random measures in R d generated by so-called germ-grain models. The germ-grain model is deened as the union of i.i.d. compact random sets (grains) shifted by points (germs) of a point process. This model gives rise to random measures deened by the sum of contributions of non-overlapping parts of the individual(More)
We consider m-dependent random elds of bounded random vectors (generated by independend random elds) and investigate the analyticity of the cumulant generating function of sums of these random vectors. Using the Kirkwood-Salsburg equations we derive upper bounds for the cumulant generating function and prove its analyticity in a neighbourhood of zero, where(More)
We derive a central limit theorem for the number of vertices of convex polytopes induced by stationary Poisson hyperplane processes in R d. This result generalizes an earlier one proved by Paroux [Adv. for intersection points of motion-invariant Poisson line processes in R 2. Our proof is based on Hoeffd-ing's decomposition of U-statistics which seems to be(More)
We give a representation of the second-order factorial moment measure of the point process of nodes (vertices of cells) associated with a stationary Voronoi tessellation in R d. If the Voronoi tessellation is generated by a stationary Poisson process this representation formula yields the corresponding pair correlation function g V (r) which can be(More)
We describe and discuss the explicit calculation of the pair correlation function of the point process of nodes associated with a three-dimensional stationary Poisson-Voronoi tessellation. Moreover, the precise asymptotics for the variance of the number of nodes in an expanding region and the variance of vertices of the typical Poisson-Voronoi polyhedron(More)
For a sequence T (1) ; T (2) ; : : : of piecewise monotonic C 2-transformations of the unit interval I onto itself, we prove exponential-mixing , an almost Markov property and other higher-order mixing properties. Furthermore, we obtain optimal rates of convergence in the central limit theorem and large deviation relations for the sequence I are of bounded(More)
We consider Johnson-Mehl tessellations generated by stationary independently marked (not necessarily Poissonian) point processes in d-dimensional Euclidean space. We rst analyze the Palm distribution of the thinned point process which coincides with the family of nuclei of non-empty Johnson-Mehl cells. This yields quite a general scheme for the construction(More)
We consider spatially homogeneous marked point patterns in an unboundedly expanding convex sampling window. Our main objective is to identify the distribution of the typical mark by constructing an asymptotic χ 2-goodness-of-fit test. The corresponding test statistic is based on a natural empirical version of the Palm mark distribution and a smoothed(More)