A standard CLT for triangles in a class of ERGs

2025/07/23 by Magnanini, Elena, Passuello, Giacomo
#05C80 #60F05 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2507.17484

Abstract

We prove a standard Central Limit Theorem for the (normalized) number of triangles in a class of Exponential Random Graphs derived from a slight modification of the edge-triangle model. Our main theorem covers the whole analyticity region of the free energy, and is based on a polynomial representation of the partition function.

Citations

• Conditional central limit theorems for exponential random graphs
• Statistics for the triangle density in ERGM and its mean-field approximation
• Normal approximation for exponential random graphs
• Limit theorems for exponential random graphs
• An introduction to large deviations for random graphs
• Stein's method for dependent random variables occurring in Statistical Mechanics

Related

• Statistics for the triangle density in ERGM and its mean-field approximation
• A local central limit theorem for the number of triangles in a random graph
• Limit theorems for exponential random graphs
• Exponential inequalities for the number of triangles in the\n Erd "os-R 'enyi random graph
• Normal approximation for exponential random graphs