2023/01/04 by Barbara Dembin, Dembin, Barbara
Biochemistry, Genetics and Molecular Biology · Computer Science · #Cell Image Analysis Techniques #FOS: Mathematics #Probability (math.PR) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2301.01632
openalex publication_date 2023/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We consider a multiscale Boolean percolation on \mathbb Rd with radius distribution μ on [1,+∞), d≥ 2. The model is defined by superposing the original Boolean percolation model with radius distribution μ with a countable number of scaled independent copies. The n-th copy is a Boolean percolation with radius distribution μ|[1,κ] rescaled by κn. We prove that under some regularity assumption on μ, the subcritical phase of the multiscale model is sharp for κ large enough. Moreover, we prove that the existence of an unbounded connected component depends only on the fractal part (and not of the balls with radius larger than 1).