Samenvatting
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.
| Originele taal-2 | Engels |
|---|---|
| Artikelnummer | 47 |
| Aantal pagina's | 57 |
| Tijdschrift | Electronic Journal of Probability |
| Volume | 25 |
| DOI's | |
| Status | Gepubliceerd - 2020 |
Financiering
*SB was partially supported by NSF grants DMS-1613072, DMS-1606839 and ARO grant W911NF-17-1-0010. The work of SD, RvdH, and SS was 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, and SS has been supported in part by the Infosys foundation, Bangalore, and by a MATRICS grant from SERB. †Department of Statistics and Operations Research, University of North Carolina Chapel Hill, USA. E-mail: [email protected] ‡Department of Mathematics, Massachusetts Institute of Technology & Microsoft Research, USA. E-mail: [email protected] §Department of Mathematics and Computer Science, Eindhoven University of Technology, Netherlands. E-mail: [email protected] ¶Department of Mathematics, Indian Institute of Science, India. E-mail: [email protected]
| Financiers | Financiernummer |
|---|---|
| National Science Foundation(NSF) | DMS-1606839, DMS-1613072 |
| University of North Carolina at Chapel Hill | |
| Technische Universiteit Eindhoven | |
| Nederlandse Organisatie voor Wetenschappelijk Onderzoek | 639.033.806, 024.002.003 |