The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 15, Number 1B (2005), 652-670.
How likely is an i.i.d. degree sequence to be graphical?
Given i.i.d. positive integer valued random variables D1,…,Dn, one can ask whether there is a simple graph on n vertices so that the degrees of the vertices are D1,…,Dn. We give sufficient conditions on the distribution of Di for the probability that this be the case to be asymptotically 0, ½ or strictly between 0 and ½. These conditions roughly correspond to whether the limit of nP(Di≥n) is infinite, zero or strictly positive and finite. This paper is motivated by the problem of modeling large communications networks by random graphs.
Ann. Appl. Probab., Volume 15, Number 1B (2005), 652-670.
First available in Project Euclid: 1 February 2005
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Arratia, Richard; Liggett, Thomas M. How likely is an i.i.d. degree sequence to be graphical?. Ann. Appl. Probab. 15 (2005), no. 1B, 652--670. doi:10.1214/105051604000000693. https://projecteuclid.org/euclid.aoap/1107271663