Limit theory for the Gilbert graph

Reitzner, Matthias; Schulte, Matthias; Thäle, Christoph (2017). Limit theory for the Gilbert graph. Advances in applied mathematics, 88, pp. 26-61. Elsevier 10.1016/j.aam.2016.12.006

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For a given homogeneous Poisson point process in Rd two points are connected by an edge if their distance is bounded by a prescribed distance parameter. The behaviour of the resulting random graph, the Gilbert graph or random geometric graph, is investigated as the intensity of the Poisson point process is increased and the distance parameter goes to zero. The asymptotic expectation and covariance structure of a class of length-power functionals are computed. Distributional limit theorems are derived that have a Gaussian, a stable or a compound Poisson limiting distribution. Finally, concentration inequalities are provided using a concentration inequality for the convex distance.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Schulte, Matthias

Subjects:

300 Social sciences, sociology & anthropology > 360 Social problems & social services
500 Science > 510 Mathematics
500 Science

ISSN:

0196-8858

Publisher:

Elsevier

Language:

English

Submitter:

Matthias Schulte

Date Deposited:

19 Mar 2018 16:55

Last Modified:

24 Oct 2019 17:21

Publisher DOI:

10.1016/j.aam.2016.12.006

BORIS DOI:

10.7892/boris.112840

URI:

https://boris.unibe.ch/id/eprint/112840

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