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arXiv · 2009.00316

Concentration on Poisson spaces via modified $\Phi$-Sobolev inequalities

Anna Gusakova·Holger Sambale·Christoph Thaele
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Abstract

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.

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Anna Gusakova, Holger Sambale, Christoph Thaele. 2020-09-01. Concentration on Poisson spaces via modified $\Phi$-Sobolev inequalities. https://doi.org/10.1016/j.spa.2021.06.009

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