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

Benedikt Jahnel; András Tóbiás; Elie Cali

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arXiv · 2003.06206

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

Benedikt Jahnel·András Tóbiás·Elie Cali

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Abstract

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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Benedikt Jahnel, András Tóbiás, Elie Cali. 2020-03-13. Phase transitions for the Boolean model of continuum percolation for Cox point processes. https://arxiv.org/abs/2003.06206

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