Advances in Applied Probability

The asymptotic size of the largest component in random geometric graphs with some applications

Ge Chen, Changlong Yao, and Tiande Guo

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Abstract

In this paper we estimate the expectation of the size of the largest component in a supercritical random geometric graph; the expectation tends to a polynomial on a rate of exponential decay. We sharpen the expectation's asymptotic result using the central limit theorem. Similar results can be obtained for the size of the biggest open cluster, and for the number of open clusters of percolation on a box, and so on.

Article information

Source
Adv. in Appl. Probab., Volume 46, Number 2 (2014), 307-324.

Dates
First available in Project Euclid: 29 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.aap/1401369696

Digital Object Identifier
doi:10.1239/aap/1401369696

Mathematical Reviews number (MathSciNet)
MR3215535

Zentralblatt MATH identifier
1296.60259

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 82B43: Percolation [See also 60K35]

Keywords
Random geometric graph percolation largest component Poisson-Boolean model number of open clusters

Citation

Chen, Ge; Yao, Changlong; Guo, Tiande. The asymptotic size of the largest component in random geometric graphs with some applications. Adv. in Appl. Probab. 46 (2014), no. 2, 307--324. doi:10.1239/aap/1401369696. https://projecteuclid.org/euclid.aap/1401369696


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