ASYMPTOTIC QUANTIZATION OF EXPONENTIAL RANDOM GRAPHS

• 成果类型: Article
• 署名作者: Yin, Mei; Rinaldo, Alessandro; Fadnavis, Sukhada
• 署名单位: University of Denver; Carnegie Mellon University; Harvard University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/16-AAP1175
• 发表日期: 2016
• 页码: 3251-3285
• 关键词: logistic regressions; social networks; logit-models; maximum-likelihood; triangles; families

摘要

We describe the asymptotic properties of the edge-triangle exponential random graph model as the natural parameters diverge along straight lines. We show that as we continuously vary the slopes of these lines, a typical graph drawn from this model exhibits quantized behavior, jumping from one complete multipartite graph to another, and the jumps happen precisely at the normal lines of a polyhedral set with infinitely many facets. As a result, we provide a complete description of all asymptotic extremal behaviors of the model.