Pubblicazioni

Autori:

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

Titolo:

Limit theorems for exponential random graphs

Anno:

2024

Tipologia prodotto:

Articolo in Rivista

Tipologia ANVUR:

Articolo su rivista

Lingua:

Inglese

Referee:

Sì

Nome rivista:

THE ANNALS OF APPLIED PROBABILITY

ISSN Rivista:

1050-5164

N° Volume:

34

Numero o Fascicolo:

5

Intervallo pagine:

4863-4898

Parole chiave:

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

Breve descrizione dei contenuti:

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.

Pagina Web:

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

Id prodotto:

141182

Handle IRIS:

11562/1137766

ultima modifica:

27 gennaio 2025

Citazione bibliografica:

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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