Gilbert's disc model with geostatistical marking
Journal article, 2018

We study a variant of Gilbert's disc model, in which discs are positioned at the points of a Poisson process in R-2 with radii determined by an underlying stationary and ergodic random field phi: R-2 -> [0, infinity), independent of the Poisson process. This setting, in which the random field is independent of the point process, is often referred to as geostatistical marking. We examine how typical properties of interest in stochastic geometry and percolation theory, such as coverage probabilities and the existence of long-range connections, differ between Gilbert's model with radii given by some random field and Gilbert's model with radii assigned independently, but with the same marginal distribution. Among our main observations we find that complete coverage of R(2 )does not necessarily happen simultaneously, and that the spatial dependence induced by the random field may both increase as well as decrease the critical threshold for percolation.

coverage probability

Continuum percolation

threshold comparison


Daniel Ahlberg

Stockholm University

Instituto Nacional de Matematica Pura E Aplicada, Rio de Janeiro

Uppsala University

Johan Tykesson

Chalmers, Mathematical Sciences, Analysis and Probability Theory

University of Gothenburg

Advances in Applied Probability

0001-8678 (ISSN) 1475-6064 (eISSN)

Vol. 50 4 1075-1094

Subject Categories

Applied Mechanics

Probability Theory and Statistics

Control Engineering



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