Show simple item record

dc.contributor.authorBordenave, Charles
HAL ID: 740473
dc.contributor.authorCaputo, Pietro
dc.contributor.authorChafaï, Djalil
HAL ID: 11025
ORCID: 0000-0002-1446-1428
dc.contributor.authorPiras, Daniele
dc.date.accessioned2017-11-29T12:27:52Z
dc.date.available2017-11-29T12:27:52Z
dc.date.issued2017
dc.identifier.issn2010-3263
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17099
dc.language.isoenen
dc.subjectRandom matrix
dc.subjectLogarithmic potential
dc.subjectOperator convergence
dc.subjectSpectral theory
dc.subjectObjective method
dc.subjectRandom Graph
dc.subjectHeavy tailed distribution
dc.subjectStable law
dc.subject.ddc519en
dc.titleSpectrum of large random Markov chains: heavy-tailed weights on the oriented complete graph
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe consider the random Markov matrix obtained by assigning i.i.d. non-negative weights to each edge of the complete oriented graph. In this study, the weights have unbounded first moment and belong to the domain of attraction of an alpha-stable law. We prove that as the dimension tends to infinity, the empirical measure of the singular values tends to a probability measure which depends only on alpha, characterized as the expected value of the spectral measure at the root of a weighted random tree. The latter is a generalized two-stage version of the Poisson weighted infinite tree (PWIT) introduced by David Aldous. Under an additional smoothness assumption, we show that the empirical measure of the eigenvalues tends to a non-degenerate isotropic probability measure depending only on alpha and supported on the unit disc of the complex plane. We conjecture that the limiting support is actually formed by a strictly smaller disc.
dc.relation.isversionofjnlnameRandom Matrices: Theory and Applications
dc.relation.isversionofjnlvol6
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2017
dc.relation.isversionofjnlpages1750006
dc.relation.isversionofdoi10.1142/S201032631750006X
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2017-12-15T15:48:52Z


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record