Journal of the Ramanujan Mathematical Society

Volume 35, Issue 2, June 2020 pp. 109–119.

Central limit theorem for statistics of subcritical configuration models

Authors: Siva Athreya and D. Yogeshwaran
Author institution:8th Mile Mysore Road, Indian Statistical Institute, Bangalore 560 059, India

Summary: 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.

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