THE ASYMPTOTIC VARIANCE OF THE GIANT COMPONENT OF CONFIGURATION MODEL RANDOM GRAPHS
成果类型：
Article
署名作者：
Ball, Frank; Neal, Peter
署名单位：
University of Nottingham; Lancaster University
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/16-AAP1225
发表日期：
2017
页码：
1057-1092
关键词：
摘要：
For a supercritical configuration model random graph, it is well known that, subject to mild conditions, there exists a unique giant component, whose size R-n is O (n), where n is the total number of vertices in the random graph. Moreover, there exists 0 < rho <= 1 such that R-n/n ->(p) rho as n -> infinity. We show that for a sequence of well behaved configuration model random graphs with a deterministic degree sequence satisfying 0 < rho < 1; there exists sigma(2) > 0, such that var(root n(R-n/n - rho)) -> sigma(2) as n -> infinity. Moreover, an explicit, easy to compute, formula is given for sigma(2). This provides a key stepping stone for computing the asymptotic variance of the size of the giant component for more general random graphs.