Open Access
2020 Concentration inequalities for functionals of Poisson cylinder processes
Anastas Baci, Carina Betken, Anna Gusakova, Christoph Thäle
Electron. J. Probab. 25: 1-27 (2020). DOI: 10.1214/20-EJP529


Random union sets $Z$ associated with stationary Poisson processes of $k$-cylinders in $\mathbb {R}^{d}$ 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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Anastas Baci. Carina Betken. Anna Gusakova. Christoph Thäle. "Concentration inequalities for functionals of Poisson cylinder processes." Electron. J. Probab. 25 1 - 27, 2020.


Received: 7 August 2019; Accepted: 3 October 2020; Published: 2020
First available in Project Euclid: 22 October 2020

Digital Object Identifier: 10.1214/20-EJP529

Primary: 60D05 , 60F10
Secondary: 52A22 , 60E15

Keywords: Boolean model , concentration inequality , cylindrical integral geometry , intrinsic volume , Poisson cylinder process , Stochastic geometry

Vol.25 • 2020
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