Gilbert's disc model with geostatistical marking

• Published in: Advances in applied probability Vol. 50; no. 4; pp. 1075 - 1094
• Main Authors: Ahlberg, Daniel, Tykesson, Johan
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.12.2018; Applied Probability Trust
• Subjects: 2013; Continuum percolation; coverage probability; cylinders; Dependence; Fields (mathematics); Geostatistics; IU S. N; Marking; Mathematics; Original Article; percolation; Percolation theory; plane; Poisson density functions; Probability; Probability Theory and Statistics; Sannolikhetsteori och statistik; Simulation; Stochastic geometry and its applications; Stochastic processes; threshold comparison; Primary 60D05; coverage probability; 60K37; Continuum percolation; 60K35; threshold comparison

We study a variant of Gilbert's disc model, in which discs are positioned at the points of a Poisson process in ℝ2 with radii determined by an underlying stationary and ergodic random field φ:ℝ2→[0,∞), independent of the Poisson process. This setting, in which the random field is independent of...