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We consider sub-critical configuration models and show that the central limittheorem for any additive statistic holds when the statistics satisfies a fourthmoment assumption, a variance lower bound and the degree sequence of graphsatisfies a growth condition. If the degree sequence is bounded, for well knownstatistics like component counts, log-partition function, and maximum cut-sizewhich are Lipschitz under addition of an edge or switchings then theassumptions reduce to linear growth condition for the variance of thestatistic. Our proof is based on an application of the central limit theoremfor martingale-difference arrays due to Mcleish (1974) to a suitableexploration process.

Central limit theorem for statistics of subcritical configuration models