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April 2019 Central limit theorems in the configuration model
A. D. Barbour, Adrian Röllin
Ann. Appl. Probab. 29(2): 1046-1069 (April 2019). DOI: 10.1214/18-AAP1425

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.

Citation

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A. D. Barbour. Adrian Röllin. "Central limit theorems in the configuration model." Ann. Appl. Probab. 29 (2) 1046 - 1069, April 2019. https://doi.org/10.1214/18-AAP1425

Information

Received: 1 October 2017; Revised: 1 July 2018; Published: April 2019
First available in Project Euclid: 24 January 2019

zbMATH: 07047444
MathSciNet: MR3910023
Digital Object Identifier: 10.1214/18-AAP1425

Subjects:
Primary: 60F05
Secondary: 05C80

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.29 • No. 2 • April 2019
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