Concentration properties of functionals of general Poisson processes are studied. Using a modified $\Phi$-Sobolev inequality a recursion scheme for moments is established, which is of independent interest. This is applied to derive moment and concentration inequalities for functionals on abstract Poisson spaces. Applications of the general results in stochastic geometry, namely Poisson cylinder models and Poisson random polytopes, are presented as well.

中文翻译：

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通过修改对泊松空间的集中 $\Phi$-Sobolev 不等式

研究了一般泊松过程泛函的浓度特性。使用修改的$\Phi$-Sobolev 不等式 建立矩的递归方案，这是独立的兴趣。这用于导出抽象泊松空间上泛函的矩不等式和浓度不等式。还介绍了一般结果在随机几何中的应用，即泊松圆柱模型和泊松随机多面体。