Continuum Percolation in a Nonstabilizing Environment

Autor:	Jahnel, Benedikt, Jhawar, Sanjoy Kumar, Vu, Anh Duc
Rok vydání:	2022
Předmět:	Mathematics - Probability primary: 60K35 60K37 secondary: 60G55 90B18
Druh dokumentu:	Working Paper
Popis:	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. Comment: 39 pages, 13 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2205.15366 Zobrazit plný text záznamu View this record from Arxiv