2022/05/30 by Jahnel, Benedikt, Jhawar, Sanjoy Kumar, Vu, Anh Duc · 1 citation
#60K37 #FOS: Mathematics #Probability (math.PR) #primary: 60K35 #secondary: 60G55 90B18
paper · doi:10.48550/arxiv.2205.15366
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 Hoffman 2005.