Central limit theorem for statistics of subcritical configuration models

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 [20] to a suitable exploration process.