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

2020/03/13 by Benedikt Jahnel, Jahnel, Benedikt, András Tóbiás +3 · 1 citation
Mathematics · Physics and Astronomy · #60G55 #60K35 #82B43 #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2003.06206

openalex publication_date 2020/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Boolean model with random radii based on Cox point processes.\nUnder a condition of stabilization for the random environment, we establish\nexistence and non-existence of subcritical regimes for the size of the cluster\nat the origin in terms of volume, diameter and number of points. Further, we\nprove uniqueness of the infinite cluster for sufficiently connected\nenvironments.\n

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• Phase transitions for the Widom--Rowlinson model in random environments

Related

• Continuum percolation in a nonstabilizing environment
• Continuum Percolation in a Nonstabilizing Environment
• Percolation results for the Continuum Random Cluster Model
• Continuum percolation for Cox point processes
• Subcritical Boolean percolation on graphs of bounded degree