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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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465234721

Digital Object Identifier
doi:10.1214/ECP.v14-1451

Mathematical Reviews number (MathSciNet)
MR2481672

Zentralblatt MATH identifier
1185.05129

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

Keywords
Random graphs

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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