Publications

Authors:

Bianchi, A.; Collet, F.; Magnanini, E.

Title:

Limit theorems for exponential random graphs

Year:

2024

Type of item:

Articolo in Rivista

Tipologia ANVUR:

Articolo su rivista

Language:

Inglese

Referee:

Sì

Name of journal:

THE ANNALS OF APPLIED PROBABILITY

ISSN of journal:

1050-5164

N° Volume:

34

Number or Folder:

5

Page numbers:

4863-4898

Keyword:

exponential random graphs; mean-field approximation; large deviations; phase transition; standard and non-standard limit theorems; Yang-Lee theorem

Short description of contents:

We consider the edge-triangle model, a two-parameter family of exponential random graphs in which dependence between edges is introduced through triangles. In the so-called replica symmetric regime, the limiting free energy exists together with a complete characterization of the phase diagram of the model. We borrow tools from statistical mechanics to obtain limit theorems for the edge density. First, we investigate the asymptotic distribution of this quantity, as the graph size tends to infinity, in the various phases. Then, we study the fluctuations of the edge density around its average value off the critical curve and formulate conjectures about the behavior at criticality based on the analysis of a mean-field approximation of the model. Some of our results can be extended with no substantial changes to more general classes of exponential random graphs.

Web page:

https://projecteuclid.org/journals/annals-of-applied-probability/volume-34/issue-5/Limit-theorems-for-exponential-random-graphs/10.1214/24-AAP2084.short

Product ID:

141182

Handle IRIS:

11562/1137766

Last Modified:

January 27, 2025

Bibliographic citation:

Bianchi, A.; Collet, F.; Magnanini, E., Limit theorems for exponential random graphs «THE ANNALS OF APPLIED PROBABILITY» , vol. 34 , n. 5 , 2024 , pp. 4863-4898

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