How likely is an i.i.d. degree sequence to be graphical?
成果类型：
Article
署名作者：
Arratia, R; Liggett, TM
署名单位：
University of Southern California; University of California System; University of California Los Angeles
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/105051604000000693
发表日期：
2005
页码：
652-670
关键词：
摘要：
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, 2 or strictly between 0 and 2. These conditions roughly correspond to whether the limit of nP(D-i greater than or equal to n) is infinite, zero or strictly positive and finite. This paper is motivated by the problem of modeling large communications networks by random graphs.