Central limit theorem for statistics of subcritical configuration models
Abstract
We consider sub-critical configuration models and show that the central limit theorem for any additive statistic holds when the statistics satisfies a fourth moment assumption, a variance lower bound and the degree sequence of 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 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 (1974) to a suitable exploration process.
Cite
@article{arxiv.1808.06778,
title = {Central limit theorem for statistics of subcritical configuration models},
author = {Siva Athreya and D. Yogeshwaran},
journal= {arXiv preprint arXiv:1808.06778},
year = {2019}
}
Comments
12 pages. Some typos have been corrected. References to some recent results, Variance lower bounds and some explicit applications are also added