Asymptotics for sparse exponential random graph models

被引：5

作者：

Yin, Mei ^{[1
]}

Zhu, Lingjiong ^{[2
]}

机构：

[1] Univ Denver, Dept Math, Denver, CO 80210 USA

[2] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

来源：

BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS | 2017年 / 31卷 / 02期

基金：

美国国家科学基金会;

关键词：

Sparse random graphs; exponential random graphs; asymptotics; CONVERGENT SEQUENCES; CLASSIFICATION; SINGULARITIES; CANCER;

D O I：

10.1214/16-BJPS319

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study the asymptotics for sparse exponential random graph models where the parameters may depend on the number of vertices of the graph. We obtain exact estimates for the mean and variance of the limiting probability distribution and the limiting log partition function of the edge (single)-star model. They are in sharp contrast to the corresponding asymptotics in dense exponential random graph models. Similar analysis is done for directed sparse exponential random graph models parametrized by edges and multiple outward stars.

引用

页码：394 / 412

页数：19

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