Filters

2020 - 20223

More filters

2022 - 20233
Reset filters

Settings

End date: 2024 × Start date: 2020 × End date: 2024 × Start date: 2020 × Subject: continuum percolation × Subject: random environment ×

Search Results

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    Sharp phase transition for Cox percolation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2022) Hirsch, Christian; Jahnel, Benedikt; Muirhead, Stephen
    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.
  • Thumbnail Image
    Item
    Phase transitions for the Boolean model of continuum percolation for Cox point processes
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Jahnel, Benedikt; Tóbiás, András; Cali, Eli
    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.
  • Thumbnail Image
    Item
    Sharp phase transition for Cox percolation
    (Seattle, Wash. : Univ. of Washington, Mathematics Dep., 2022) Hirsch, Christian; Jahnel, Benedikt; Muirhead, Stephen
    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, satisfies a local boundedness condition and can be constructed from a discrete iid random field, however the FKG inequality need not hold. The proof combines the OSSS inequality with a coarse-graining construction that allows us to compare different notions of influence.