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Central limit theorem for statistics of subcritical configuration models
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Central limit theorem for statistics of subcritical configuration models
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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.
Forward citations
Cited by 3 Pith papers
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Normal approximation of the numbers of isolated edges and isolated 2-stars in uniform simple graphs with given vertex degrees
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Normal approximation of the numbers of isolated edges and isolated 2-stars in uniform simple graphs with given vertex degrees
Establishes the first finite-sample normal approximation bounds for isolated edges and isolated 2-stars in uniform simple graphs with given degrees via new Stein's method and coupling.
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