Brazilian Journal of Probability and Statistics

Asymptotics for sparse exponential random graph models

Mei Yin and Lingjiong Zhu

Full-text: Open access

Abstract

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.

Article information

Source
Braz. J. Probab. Stat., Volume 31, Number 2 (2017), 394-412.

Dates
Received: September 2015
Accepted: April 2016
First available in Project Euclid: 14 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1492156969

Digital Object Identifier
doi:10.1214/16-BJPS319

Mathematical Reviews number (MathSciNet)
MR3635912

Zentralblatt MATH identifier
1365.05264

Keywords
Sparse random graphs exponential random graphs asymptotics

Citation

Yin, Mei; Zhu, Lingjiong. Asymptotics for sparse exponential random graph models. Braz. J. Probab. Stat. 31 (2017), no. 2, 394--412. doi:10.1214/16-BJPS319. https://projecteuclid.org/euclid.bjps/1492156969


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