DOI: 10.1112/blms.70464 ISSN: 0024-6093
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 PfenningerAbstract
In this note we outline a new and simple approach to proving central limit theorems for various ‘global’ graph parameters that 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 ‐core for sparse random graphs.