Show simple item record

hal.structure.identifierInria Paris-Rocquencourt
dc.contributor.authorCoste, Simon
HAL ID: 743731
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorSalez, Justin
HAL ID: 2772
dc.date.accessioned2021-09-25T09:18:51Z
dc.date.available2021-09-25T09:18:51Z
dc.date.issued2021
dc.identifier.issn2168-894X
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/21828
dc.language.isoenen
dc.subjectextended statesen
dc.subjectsparse Erdős–Rényi random graphsen
dc.subjectspectrumen
dc.subjectunimodular Galton–Watson treesen
dc.subject.ddc519en
dc.titleEmergence of extended states at zero in the spectrum of sparse random graphsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe confirm the long-standing prediction that c=e≈2.718 is the threshold for the emergence of a nonvanishing absolutely continuous part (extended states) at zero in the limiting spectrum of the Erdős–Rényi random graph with average degree c. This is achieved by a detailed second-order analysis of the resolvent (A−z)−1 near the singular point z=0, where A is the adjacency operator of the Poisson–Galton–Watson tree with mean offspring c. More generally, our method applies to arbitrary unimodular Galton–Watson trees, yielding explicit criteria for the presence or absence of extended states at zero in the limiting spectral measure of a variety of random graph models, in terms of the underlying degree distribution.en
dc.relation.isversionofjnlnameAnnals of Probability
dc.relation.isversionofjnlvol49en
dc.relation.isversionofjnlissue4en
dc.relation.isversionofjnldate2021-07
dc.relation.isversionofjnlpages2012-2030en
dc.relation.isversionofdoi10.1214/20-AOP1499en
dc.relation.isversionofjnlpublisherInstitute of Mathematical Statisticsen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2021-09-25T09:13:04Z
hal.author.functionaut
hal.author.functionaut


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record