PREFERENTIAL ATTACHMENT WITHOUT VERTEX GROWTH: EMERGENCE OF THE GIANT COMPONENT

• 成果类型: Article
• 署名作者: Janson, Svante; Warnke, Lutz
• 署名单位: Uppsala University; University System of Georgia; Georgia Institute of Technology
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/20-AAP1610
• 发表日期: 2021
• 页码: 1523-1547
• 关键词: Random graphs; LIMIT-THEOREMS; percolation; EVOLUTION

摘要

We study the following preferential attachment variant of the classical Erd os-Renyi random graph process. Starting with an empty graph on n vertices, new edges are added one-by-one, and each time an edge is chosen with probability roughly proportional to the product of the current degrees of its endpoints (note that the vertex set is fixed). We determine the asymptotic size of the giant component in the supercritical phase, confirming a conjecture of Pittel from 2010. Our proof uses a simple method: we condition on the vertex degrees (of a multigraph variant), and use known results for the configuration model.