2006/11/10 by Alexis Gillett, A. Gillett, Gillett, A. +3
Mathematics · Physics and Astronomy · #60K35 #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60K35
paper · pdf · doi:10.48550/arxiv.math/0611315
18 pages
arxiv created 2006/11/10 · openalex publication_date 2006/11/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a continuum percolation model defined on the points of a d-dimensional homogeneous Poisson process. Each Poisson point is connected to all points within its connection range, which depends on the distances to the other Poisson points. We show that the new model exhibits a phase transition, and obtain results about the critical values in low and high dimensions.