WIAS Preprint No. 2704, (2020)

Phase transitions for the Boolean model of continuum percolation for Cox point processes


  • Jahnel, Benedikt
    ORCID: 0000-0002-4212-0065
  • Tóbiás, András
  • Cali, Eli

2010 Mathematics Subject Classification

  • 82B43 60G55 60K35


  • Cox point processes, continuum percolation, random environment, Boolean model, Gilbert disk model, random radii, moments, diameter of cluster, volume of cluster, number of points in cluster, uniqueness of infinite cluster, complete coverage, ergodicity, stabilization, exponential stabilization, polynomial stabilization, b-dependence, essential connectedness, shot-noise fields, Boolean models on Boolean models




We consider the Boolean model with random radii based on Cox point processes. Under a condition of stabilization for the random environment, we establish existence and non-existence of subcritical regimes for the size of the cluster at the origin in terms of volume, diameter and number of points. Further, we prove uniqueness of the infinite cluster for sufficiently connected environments.

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