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Gilbert´s disc model with geostatical marking
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory. Inst Nacl Matemat Pura & Aplicada, Rio De Janeiro, RJ, Brazil;Stockholm Univ, Dept Math, SE-10691 Stockholm, Sweden;Stockholm Univ, Dept Math, SE-10691 Stockholm, Sweden.
Chalmers Univ Technol, Dept Math, SE-41296 Gothenburg, Sweden;Univ Gothenburg, Gothenburg, Sweden.
2018 (English)In: Advances in Applied Probability, ISSN 0001-8678, E-ISSN 1475-6064, Vol. 50, no 4, p. 1075-1094Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
APPLIED PROBABILITY TRUST , 2018. Vol. 50, no 4, p. 1075-1094
Keywords [en]
Continuum percolation, coverage probability, threshold comparison
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-372379DOI: 10.1017/apr.2018.51ISI: 000451616400003OAI: oai:DiVA.org:uu-372379DiVA, id: diva2:1276697
Funder
Swedish Research Council, 637-2013-7302Knut and Alice Wallenberg FoundationAvailable from: 2019-01-08 Created: 2019-01-08 Last updated: 2019-01-08Bibliographically approved

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Ahlberg, Daniel

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