How likely is an i.i.d. degree sequence to be graphical?
| dc.creator | Arratia, Richard | |
| dc.creator | Liggett, Thomas M. | |
| dc.date | 2005-04-06 | |
| dc.date.accessioned | 2026-07-07T05:18:49Z | |
| dc.date.available | 2026-07-07T05:18:49Z | |
| dc.description | 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. | |
| dc.description | 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) | |
| dc.identifier | https://arxiv.org/abs/math/0504096 | |
| dc.identifier | http://arxiv.org/abs/math/0504096 | |
| dc.identifier | Annals of Applied Probability 2005, Vol. 15, No. 1B, 652-670 | |
| dc.identifier | doi:10.1214/105051604000000693 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74802 | |
| dc.subject | Probability | |
| dc.subject | 05C07, 05C80, 60G70. (Primary) | |
| dc.title | How likely is an i.i.d. degree sequence to be graphical? | |
| dc.type | text |