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Subject: moments × WGL Institute: WIAS ×

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    Catalytic branching processes via spine techniques and renewal theory
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Döring, Leif; Roberts, Matthew I.
    In this article we contribute to the moment analysis of branching processes in catalytic media. The many-to-few lemma based on the spine technique is used to derive a system of (discrete space) partial differential equations for the number of particles in a variation of constants formulation. The long-time behavior is then deduced from renewal theorems and induction.
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    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.