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

TL;DR

This paper develops new concentration inequalities for functionals of Poisson processes using a modified $\

Contribution

It introduces a modified $\\Phi$-Sobolev inequality and a recursion scheme for moments, advancing the analysis of Poisson process functionals.

Findings

Derived new moment inequalities for Poisson functionals

Established concentration bounds for stochastic geometry models

Applied results to Poisson cylinder models and random polytopes

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.