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

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.

Keywords

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

URI

https://oa.tib.eu/renate/handle/123456789/9354
https://doi.org/10.34657/8392

Citation

Jahnel, B., Tóbiás, A., & Cali, E. (2020). Phase transitions for the Boolean model of continuum percolation for Cox point processes (Vol. 2704). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik. https://doi.org//10.20347/WIAS.PREPRINT.2704

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Mathematik

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