Universality for critical heavy-tailed network models: Metric structure of maximal components
Shankar Bhamidi, Souvik Dhara, Remco van der Hofstad, Sanchayan Sen
TL;DR
This paper investigates the metric structure of the largest components in critical heavy-tailed networks, establishing universal scaling limits and refined asymptotics for susceptibility and diameter across different models.
Contribution
It develops general principles to extend known results from rank-one inhomogeneous random graphs to broader classes of heavy-tailed network models.
Findings
Identifies universal scaling limits for maximal components
Provides refined asymptotics for susceptibility functions
Analyzes the maximal diameter in the barely subcritical regime
Abstract
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 [Probab. Theory Relat. Fields 2018]. We develop general principles under which the identical scaling limits as the rank-one case 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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