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• W3105356453 abstract "We study a variant of Gilbert's disc model, in which discs are positioned at the points of a Poisson process in $mathbb{R}^2$ with radii determined by an underlying stationary and ergodic random field $varphi:mathbb{R}^2to[0,infty)$, independent of the Poisson process. When the random field is independent of the point process one often talks about '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 $mathbb{R}^2$ 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." @default.
• W3105356453 created "2020-11-23" @default.
• W3105356453 creator A5027831489 @default.
• W3105356453 creator A5078775076 @default.
• W3105356453 date "2018-11-29" @default.
• W3105356453 modified "2023-09-27" @default.
• W3105356453 title "Gilbert's disc model with geostatistical marking" @default.
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• W3105356453 doi "https://doi.org/10.1017/apr.2018.51" @default.
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