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Author: Jahnel, Benedikt × Start date: 2020 × End date: 2024 × Start date: 2020 × Type: Text × Version: publishedVersion × Subject: Poisson point process × WGL Institute: WIAS ×

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Now showing 1 - 4 of 4
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    Exponential Moments for Planar Tessellations
    (New York, NY [u.a.] : Springer Science + Business Media B.V., 2020) Jahnel, Benedikt; Tóbiás, András
    In this paper we show existence of all exponential moments for the total edge length in a unit disk for a family of planar tessellations based on stationary point processes. Apart from classical tessellations such as the Poisson–Voronoi, Poisson–Delaunay and Poisson line tessellation, we also treat the Johnson–Mehl tessellation, Manhattan grids, nested versions and Palm versions. As part of our proofs, for some planar tessellations, we also derive existence of exponential moments for the number of cells and the number of edges intersecting the unit disk.
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    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.
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    Stochastic homogenization on irregularly perforated domains
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Heida, Martin; Jahnel, Benedikt; Vu, Anh Duc
    We study stochastic homogenization of a quasilinear parabolic PDE with nonlinear microscopic Robin conditions on a perforated domain. The focus of our work lies on the underlying geometry that does not allow standard homogenization techniques to be applied directly. Instead we prove homogenization on a regularized geometry and demonstrate afterwards that the form of the homogenized equation is independent from the regularization. Then we pass to the regularization limit to obtain the anticipated limit equation. Furthermore, we show that Boolean models of Poisson point processes are covered by our approach.
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    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.