# 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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