COMPONENT SIZES FOR LARGE QUANTUM ERDOS-RENYI GRAPH NEAR CRITICALITY

• 成果类型: Article
• 署名作者: Dembo, Amir; Levit, Anna; Vadlamani, Sreekar
• 署名单位: Stanford University; Stanford University; University of British Columbia; Tata Institute of Fundamental Research (TIFR); TIFR Centre for Applicable Mathematics (CAM), Bengaluru
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/17-AOP1209
• 发表日期: 2019
• 页码: 1185-1219
• 关键词: phase-transition; SCALING LIMITS

摘要

The N vertices of a quantum random graph are each a circle independently punctured at Poisson points of arrivals, with parallel connections derived through for each pair of these punctured circles by yet another independent Poisson process. Considering these graphs at their critical parameters, we show that the joint law of the rescaled by N-2/3 and ordered sizes of their connected components, converges to that of the ordered lengths of excursions above zero for a reflected Brownian motion with drift. Thereby, this work forms the first example of an inhomogeneous random graph, beyond the case of effectively rank-1 models, which is rigorously shown to be in the Erdos-Renyi graphs universality class in terms of Aldous's results.