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

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Given 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.
Published 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)

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Probability, 05C07, 05C80, 60G70. (Primary)

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http://salesiana.dossiersoluciones.com/handle/123456789/74802

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0504096
 http://arxiv.org/abs/math/0504096
 Annals of Applied Probability 2005, Vol. 15, No. 1B, 652-670
 doi:10.1214/105051604000000693

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arXiv