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arXiv · 2506.11651

A short proof of a central limit theorem for the order of the giant component and $k$-core

Michael Anastos·Joshua Erde·Mihyun Kang·Vincent Pfenninger
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Abstract

In this note we outline a new and simple approach to proving central limit theorems for various 'global' graph parameters which have robust 'local' approximations, using the Efron--Stein inequality, which relies on a combinatorial analysis of the stability of these approximations under resampling an edge. As an application, we give short proofs of a central limit theorem for the order of the giant component and of the $k$-core for sparse random graphs.

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Michael Anastos, Joshua Erde, Mihyun Kang, Vincent Pfenninger. 2025-06-13. A short proof of a central limit theorem for the order of the giant component and $k$-core. https://arxiv.org/abs/2506.11651

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