How likely is an i.i.d. degree sequence to be graphical?

dc.creatorArratia, Richard
dc.creatorLiggett, Thomas M.
dc.date2005-04-06
dc.date.accessioned2026-07-07T05:18:49Z
dc.date.available2026-07-07T05:18:49Z
dc.descriptionGiven i.i.d. positive integer valued random variables D_1,...,D_n, one can ask whether there is a simple graph on n vertices so that the degrees of the vertices are D_1,...,D_n. We give sufficient conditions on the distribution of D_i for the probability that this be the case to be asymptotically 0, {1/2} or strictly between 0 and {1/2}. These conditions roughly correspond to whether the limit of nP(D_i\geq n) is infinite, zero or strictly positive and finite. This paper is motivated by the problem of modeling large communications networks by random graphs.
dc.descriptionPublished at http://dx.doi.org/10.1214/105051604000000693 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0504096
dc.identifierhttp://arxiv.org/abs/math/0504096
dc.identifierAnnals of Applied Probability 2005, Vol. 15, No. 1B, 652-670
dc.identifierdoi:10.1214/105051604000000693
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74802
dc.subjectProbability
dc.subject05C07, 05C80, 60G70. (Primary)
dc.titleHow likely is an i.i.d. degree sequence to be graphical?
dc.typetext

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