THE COMPONENT SIZES OF A CRITICAL RANDOM GRAPH WITH GIVEN DEGREE SEQUENCE

• 成果类型: Article
• 署名作者: Joseph, Adrien
• 署名单位: Sorbonne Universite; Universite Paris Cite
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/13-AAP985
• 发表日期: 2014
• 页码: 2560-2594
• 关键词: giant component; SCALING LIMITS

摘要

Consider a critical random multigraph G(n) with n vertices constructed by the configuration model such that its vertex degrees are independent random variables with the same distribution v (criticality means that the second moment of v is finite and equals twice its first moment). We specify the scaling limits of the ordered sequence of component sizes of G(n) as n tends to infinity in different cases. When v has finite third moment, the components sizes rescaled by n(-2/3) converge to the excursion lengths of a Brownian motion with parabolic drift above past minima, whereas when v is a power law distribution with exponent gamma is an element of(3, 4), the components sizes rescaled by n(-(gamma-2)/(gamma-1)) converge to the excursion lengths of a certain nontrivial drifted process with independent increments above past minima. We deduce the asymptotic behavior of the component sizes of a critical random simple graph when v has finite third moment.