CENTRAL LIMIT THEOREMS IN THE CONFIGURATION MODEL

• 成果类型: Article
• 署名作者: Barbour, A. D.; Rollin, Adrian
• 署名单位: University of Zurich; National University of Singapore
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/18-AAP1425
• 发表日期: 2019
• 页码: 1046-1069
• 关键词: Asymptotic Normality; giant component; graphs

摘要

We prove a general normal approximation theorem for local graph statistics in the configuration model, together with an explicit bound on the error in the approximation with respect to the Wasserstein metric. Such statistics take the form T := Sigma(v is an element of V) H-v, where V is the vertex set, and H-v depends on a neighbourhood in the graph around v of size at most l. The error bound is expressed in terms of l, vertical bar V vertical bar, an almost sure bound on H-v, the maximum vertex degree d(max) and the variance of T. Under suitable assumptions on the convergence of the empirical degree distributions to a limiting distribution, we deduce that the size of the giant component in the configuration model has asymptotically Gaussian fluctuations.