Universality for critical heavy-tailed network models: Metric structure of maximal components
arXiv:1703.07145 · doi:10.1214/19-EJP408
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.
Final published version. 47 pages, 6 figures
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