Continuum percolation in high dimensions

Details Continuum percolation in high dimensions Continuum percolation in high dimensions

2011-08-31

arxiv.org/abs/1108.6133v1

Mathematics

Probability

25 pages, 3 figures

Scientific paper

Consider a Boolean model $\Sigma$ in $\R^d$, where the centers are given by a homogeneous Poisson point process with intensity $\lambda$ and the radii of distinct balls are i.i.d. \ with common distribution $\nu$. Some numerical simulations and some heuristic arguments suggest that the critical covered volume $c^c_d(\nu)$, which is the proportion of space covered by $\Sigma$ at critical intensity, may be minimal when $\nu$ is a Dirac measure.

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