Concentration inequalities for functionals of Poisson cylinder processes

2019/08/06 by Baci, Anastas, Betken, Carina, Gusakova, Anna +1
#60E15 #60F10 #FOS: Mathematics #Primary 60D05 #Probability (math.PR) #Secondary 52A22

paper · doi:10.48550/arxiv.1908.02112

Abstract

Random union sets Z associated with stationary Poisson processes of k-cylinders in ℝ^d are considered. Under general conditions on the typical cylinder base a concentration inequality for the volume of Z restricted to a compact window is derived. Assuming convexity of the typical cylinder base and isotropy of Z a concentration inequality for intrinsic volumes of arbitrary order is established. A number of special cases are discussed, for example the case when the cylinder bases arise from a random rotation of a fixed convex body. Also the situation of expanding windows is studied. Special attention is payed to the case k=0, which corresponds to the classical Boolean model.

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