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June 2014 The asymptotic size of the largest component in random geometric graphs with some applications
Ge Chen, Changlong Yao, Tiande Guo
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Adv. in Appl. Probab. 46(2): 307-324 (June 2014). DOI: 10.1239/aap/1401369696

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.

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Ge Chen. Changlong Yao. Tiande Guo. "The asymptotic size of the largest component in random geometric graphs with some applications." Adv. in Appl. Probab. 46 (2) 307 - 324, June 2014. https://doi.org/10.1239/aap/1401369696

Information

Published: June 2014
First available in Project Euclid: 29 May 2014

zbMATH: 1296.60259
MathSciNet: MR3215535
Digital Object Identifier: 10.1239/aap/1401369696

Subjects:
Primary: 60K35
Secondary: 60D05, 82B43

Rights: Copyright © 2014 Applied Probability Trust

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Vol.46 • No. 2 • June 2014
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