WIAS Preprint No. 2445, (2017)

Continuum percolation for Cox point processes



Authors

  • Hirsch, Christian
  • Jahnel, Benedikt
    ORCID: 0000-0002-4212-0065
  • Cali, Elie

2010 Mathematics Subject Classification

  • 60F10 60K35

Keywords

  • Cox processes, percolation, stabilization, large deviations

DOI

10.20347/WIAS.PREPRINT.2445

Abstract

We investigate continuum percolation for Cox point processes, that is, Poisson point processes driven by random intensity measures. First, we derive sufficient conditions for the existence of non-trivial sub- and super-critical percolation regimes based on the notion of stabilization. Second, we give asymptotic expressions for the percolation probability in large-radius, high-density and coupled regimes. In some regimes, we find universality, whereas in others, a sensitive dependence on the underlying random intensity measure survives.

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