Open Access
2020 Universality for critical heavy-tailed network models: Metric structure of maximal components
Shankar Bhamidi, Souvik Dhara, Remco van der Hofstad, Sanchayan Sen
Electron. J. Probab. 25: 1-57 (2020). DOI: 10.1214/19-EJP408


We study limits of the largest connected components (viewed as metric spaces) obtained by critical percolation on uniformly chosen graphs and configuration models with heavy-tailed degrees. For rank-one inhomogeneous random graphs, such results were derived by Bhamidi, van der Hofstad, Sen (2018) [15]. We develop general principles under which the identical scaling limits as in [15] can be obtained. Of independent interest, we derive refined asymptotics for various susceptibility functions and the maximal diameter in the barely subcritical regime.


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Shankar Bhamidi. Souvik Dhara. Remco van der Hofstad. Sanchayan Sen. "Universality for critical heavy-tailed network models: Metric structure of maximal components." Electron. J. Probab. 25 1 - 57, 2020.


Received: 5 February 2019; Accepted: 22 December 2019; Published: 2020
First available in Project Euclid: 24 April 2020

zbMATH: 1445.60015
MathSciNet: MR4092766
Digital Object Identifier: 10.1214/19-EJP408

Primary: 05C80 , 60C05

Keywords: Critical configuration model , Critical percolation , Gromov-weak convergence , heavy-tailed degrees , multiplicative coalescent , Universality

Vol.25 • 2020
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