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arXiv · 1703.04971

Concentration inequalities for measures of a Boolean model

Günter Last·Fabian Gieringer
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Abstract

We consider a Boolean model $Z$ driven by a Poisson particle process $\eta$ on a metric space $\mathbb{Y}$. We study the random variable $\rho(Z)$, where $\rho$ is a (deterministic) measure on $\mathbb{Y}$. Due to the interaction of overlapping particles, the distribution of $\rho(Z)$ cannot be described explicitly. In this note we derive concentration inequalities for $\rho(Z)$. To this end we first prove two concentration inequalities for functions of a Poisson process on a general phase space.

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Günter Last, Fabian Gieringer. 2017-03-15. Concentration inequalities for measures of a Boolean model. https://arxiv.org/abs/1703.04971

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