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2009 A local limit theorem for the critical random graph
Remco van der Hofstad, Wouter Kager, Tobias Müller
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Electron. Commun. Probab. 14: 122-131 (2009). DOI: 10.1214/ECP.v14-1451


We consider the limit distribution of the orders of the $k$ largest components in the Erdos-Rényi random graph inside the "critical window" for arbitrary $k$. We prove a local limit theorem for this joint distribution and derive an exact expression for the joint probability density function.


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Remco van der Hofstad. Wouter Kager. Tobias Müller. "A local limit theorem for the critical random graph." Electron. Commun. Probab. 14 122 - 131, 2009.


Accepted: 19 February 2009; Published: 2009
First available in Project Euclid: 6 June 2016

zbMATH: 1185.05129
MathSciNet: MR2481672
Digital Object Identifier: 10.1214/ECP.v14-1451

Primary: 05C80

Keywords: Random graphs

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