WIAS Preprint No. 2943, (2022)

Continuum percolation in a nonstabilizing environment


Authors

  • Jahnel, Benedikt
    ORCID: 0000-0002-4212-0065
  • Jhawar, Sanjoy Kumar
    ORCID: 0000-0003-1297-0525
  • Vu, Anh Duc
    ORCID: 0009-0005-6913-4992

2020 Mathematics Subject Classification

  • 60K35 60K37

Keywords

  • Boolean model, Cox point process, Manhattan grid, discretization, phase transition

DOI

10.20347/WIAS.PREPRINT.2943

Abstract

We prove nontrivial phase transitions for continuum percolation in a Boolean model based on a Cox point process with nonstabilizing directing measure. The directing measure, which can be seen as a stationary random environment for the classical Poisson--Boolean model, is given by a planar rectangular Poisson line process. This Manhattan grid type construction features long-range dependencies in the environment, leading to absence of a sharp phase transition for the associated Cox--Boolean model. Our proofs rest on discretization arguments and a comparison to percolation on randomly stretched lattices established in [MR2116736].

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