Electronic Communications in Probability

A local limit theorem for the critical random graph

Remco van der Hofstad, Wouter Kager, and Tobias Müller

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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.

Article information

Electron. Commun. Probab., Volume 14 (2009), paper no. 12, 122-131.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05C80: Random graphs [See also 60B20]

Random graphs

This work is licensed under aCreative Commons Attribution 3.0 License.


van der Hofstad, Remco; Kager, Wouter; Müller, Tobias. A local limit theorem for the critical random graph. Electron. Commun. Probab. 14 (2009), paper no. 12, 122--131. doi:10.1214/ECP.v14-1451. https://projecteuclid.org/euclid.ecp/1465234721

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