WIAS Preprint No. 2922, (2022)

Sharp phase transition for Cox percolation


Authors

  • Hirsch, Christian
  • Jahnel, Benedikt
    ORCID: 0000-0002-4212-0065
  • Muirhead, Stephen

2020 Mathematics Subject Classification

  • 60F10 60K35

Keywords

  • Cox point process, OSSS inequality, continuum percolation, Poisson point process, random environment, Delaunay tessellation

DOI

10.20347/WIAS.PREPRINT.2922

Abstract

We prove the sharpness of the percolation phase transition for a class of Cox percolation models, i.e., models of continuum percolation in a random environment. The key requirements are that the environment has a finite range of dependence and satisfies a local boundedness condition, however the FKG inequality need not hold. The proof combines the OSSS inequality with a coarse-graining construction.

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