Central limit theorems in the configuration model

Abstract

We prove a general normal approximation theorem for local graph statistics in the configuration model, together with an explicit bound on the error in the approximation with respect to the Wasserstein metric. Such statistics take the form $T:={\sum }_{v\in V}{H}_v$, where $V$ is the vertex set, and $H_v$ depends on a neighbourhood in the graph around $v$ of size at most $\ell$. The error bound is expressed in terms of $\ell$, $|V|$, an almost sure bound on $H_v$, the maximum vertex degree $d_{\max }$ and the variance of $T$. Under suitable assumptions on the convergence of the empirical degree distributions to a limiting distribution, we deduce that the size of the giant component in the configuration model has asymptotically Gaussian fluctuations.

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References in corpus (4)

• Asymptotic normality of the $k$-core in random graphs
• Stein couplings for normal approximation
• Functional Central Limit Theorem For Susceptible-Infected Process On Configuration Model Graphs
• Central limit theorem for statistics of subcritical configuration models

Cited by in corpus (2)

• Mixing Time of Vertex-Weighted Exponential Random Graphs
• Central limit theorem for statistics of subcritical configuration models