Open Access
2022 Global lower mass-bound for critical configuration models in the heavy-tailed regime
Shankar Bhamidi, Souvik Dhara, Remco van der Hofstad, Sanchayan Sen
Author Affiliations +
Electron. J. Probab. 27: 1-29 (2022). DOI: 10.1214/22-EJP821


We establish the global lower mass-bound property for the largest connected components in the critical window for the configuration model when the degree distribution has an infinite third moment. The scaling limit of the critical percolation clusters, viewed as measured metric spaces, was established in our prior work with respect to the Gromov-weak topology. Our result extends those scaling limit results to the stronger Gromov-Hausdorff-Prokhorov topology under slightly stronger assumptions on the degree distribution. This implies the distributional convergence of global functionals such as the diameter of the largest critical components. Further, our result gives a sufficient condition for compactness of the random metric spaces that arise as scaling limits of critical clusters in the heavy-tailed regime.

Funding Statement

The authors are grateful to two anonymous referees for their careful reading and many comments and suggestions on an earlier version of the paper. SB was partially supported by NSF grants DMS-1613072, DMS-1606839, and ARO grant W911NF-17-1-0010. SD and RvdH were supported by the Netherlands Organisation for Scientific Research (NWO) through Gravitation Networks grant 024.002.003. In addition, RvdH was supported by VICI grant 639.033.806. SD also thanks Elchanan Mossel for supporting his research through Vannevar Bush Faculty Fellowship (ONR-N00014-20-1-2826), Simons Investigator award (622132). SS has been supported in part by the Infosys foundation, Bangalore, and by MATRICS grant MTR/2019/000745 from SERB. SD thanks Eindhoven University of Technology, where a major part of this work was done.


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Shankar Bhamidi. Souvik Dhara. Remco van der Hofstad. Sanchayan Sen. "Global lower mass-bound for critical configuration models in the heavy-tailed regime." Electron. J. Probab. 27 1 - 29, 2022.


Received: 8 May 2020; Accepted: 3 July 2022; Published: 2022
First available in Project Euclid: 3 August 2022

MathSciNet: MR4460270
zbMATH: 1507.60019
Digital Object Identifier: 10.1214/22-EJP821

Primary: 05C80 , 60C05

Keywords: Critical configuration model , global lower mass-bound , heavy-tailed degrees

Vol.27 • 2022
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