2024/12/04 by Jahnel, Benedikt, Jhawar, Sanjoy Kumar, Vu, Anh Duc
#500 Naturwissenschaften und Mathematik::510 Mathematik::519 Wahrscheinlichkeiten #Boolean model #Cox point process #Manhattan grid #angewandte Mathematik #discretization #phase transition
paper · doi:10.14279/depositonce-22346
We prove phase transitions for continuum percolation in a Boolean model based on a Cox point process with nonstabilizing directing measure. The directing measure, which can be seen as a stationary random environment for the classical Poisson–Boolean model, is given by a planar rectangular Poisson line process. This Manhattan grid type construction features long-range dependencies in the environment, leading to absence of a sharp phase transition for the associated Cox–Boolean model. The phase transitions are established under individually as well as jointly varying parameters. Our proofs rest on discretization arguments and a comparison to percolation on randomly stretched lattices established in [Hof05].