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dc.contributor.authorDhara, Souvik
dc.contributor.authorvan der Hofstad, Remco
dc.contributor.authorvan Leeuwaarden, Johan S. H.
dc.date.accessioned2021-09-20T17:41:26Z
dc.date.available2021-09-20T17:41:26Z
dc.date.issued2021-02-17
dc.identifier.urihttps://hdl.handle.net/1721.1/132012
dc.description.abstractAbstract In this paper, we study the critical behavior of percolation on a configuration model with degree distribution satisfying an infinite second-moment condition, which includes power-law degrees with exponent $$\tau \in (2,3)$$ τ ∈ ( 2 , 3 ) . It is well known that, in this regime, many canonical random graph models, such as the configuration model, are robust in the sense that the giant component is not destroyed when the percolation probability stays bounded away from zero. Thus, the critical behavior is observed when the percolation probability tends to zero with the network size, despite of the fact that the average degree remains bounded. In this paper, we initiate the study of critical random graphs in the infinite second-moment regime by identifying the critical window for the configuration model. We prove scaling limits for component sizes and surplus edges, and show that the maximum diameter the critical components is of order $$\log n$$ log n , which contrasts with the previous universality classes arising in the literature. This introduces a third and novel universality class for the critical behavior of percolation on random networks, that is not covered by the multiplicative coalescent framework due to Aldous and Limic (Electron J Probab 3(3):1–59, 1998). We also prove concentration of the component sizes outside the critical window, and that a unique, complex giant component emerges after the critical window. This completes the picture for the percolation phase transition on the configuration model.en_US
dc.publisherSpringer Berlin Heidelbergen_US
dc.relation.isversionofhttps://doi.org/10.1007/s00220-021-03957-8en_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.sourceSpringer Berlin Heidelbergen_US
dc.titleCritical Percolation on Scale-Free Random Graphs: New Universality Class for the Configuration Modelen_US
dc.typeArticleen_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematics
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2021-03-02T04:48:37Z
dc.language.rfc3066en
dc.rights.holderThe Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature
dspace.embargo.termsY
dspace.date.submission2021-03-02T04:48:37Z
mit.licensePUBLISHER_POLICY
mit.metadata.statusAuthority Work and Publication Information Needed


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