Critical fluctuations in the edge--triangle exponential random graph models

We prove quantitative limit theorems for the edge density $Q$ in the dense edge--triangle exponential random graph model at criticality and under parameter perturbations of order $n^{-1}$. At the fixed critical parameters $(α_c,h_c),$ the centered fluctuations satisfy $n^{2/3}(Q-\mathbb{E} Q)\Righta