RANKINGS IN DIRECTED CONFIGURATION MODELS WITH HEAVY TAILED IN-DEGREES

• 成果类型: Article
• 署名作者: Cai, Xing shi; Caputo, Pietro; Perarnau, Guillem; Quattropani, Matteo
• 署名单位: Duke Kunshan University; Roma Tre University; Centre de Recerca Matematica (CRM); Universitat Politecnica de Catalunya; Sapienza University Rome
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP1955
• 发表日期: 2023
• 页码: 5613-5667
• 关键词: random-walks; giant component; pagerank; cutoff; probabilities; continuity; distances; time

摘要

We consider the extremal values of the stationary distribution of sparse directed random graphs with given degree sequences and their relation to the extremal values of the in-degree sequence. The graphs are generated by the directed configuration model. Under the assumption of bounded (2 + eta)moments on the in-degrees and of bounded out-degrees, we obtain tight comparisons between the maximum value of the stationary distribution and the maximum in-degree. Under the further assumption that the order statistics of the in-degrees have a power-law behavior, we show that the extremal values of the stationary distribution also have a power-law behavior with the same index. In the same setting, we prove that these results extend to the PageRank scores of the random digraph, thus confirming a version of the socalled power-law hypothesis. Along the way we establish several facts about the model, including the mixing time cutoff and the characterization of the typical values of the stationary distribution, which were previously obtained under the assumption of bounded in-degrees.