Central limit theorem for statistics of subcritical configuration models
Journal of the Ramanujan Mathematical Society
We consider subcritical configuration models and show that the central limit theorem for any additive statistic holds when the statistic satisfies a fourth moment assumption, a variance lower bound and the degree sequence of the graph satisfies a growth condition. If the degree sequence is bounded, for well known statistics like component counts, log-partition function, and maximum cut-size which are Lipschitz under addition of an edge or switchings then the assumptions reduce to a linear growth condition for the variance of the statistic. Our proof is based on an application of the central limit theorem for martingale-difference arrays due to McLeish  to a suitable exploration process.
Athreya, Siva and Yogeshwaran, D., "Central limit theorem for statistics of subcritical configuration models" (2020). Journal Articles. 253.