A short proof of a central limit theorem for the order of the giant component and k-core Anastos, Michael Erde, Joshua Kang, Mihyun Pfenninger, Vincent ddc:510 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 𝑘 -core for sparse random graphs. Wiley 2026 info:eu-repo/semantics/article doc-type:Article Article http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/22752 https://research-explorer.ista.ac.at/download/22752/22845 Anastos M, Erde J, Kang M, Pfenninger V. A short proof of a central limit theorem for the order of the giant component and k-core. <i>Bulletin of the London Mathematical Society</i>. 2026;58(8). doi:<a href="https://doi.org/10.1112/blms.70464">10.1112/blms.70464</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1112/blms.70464 info:eu-repo/semantics/altIdentifier/issn/0024-6093 info:eu-repo/semantics/altIdentifier/e-issn/1469-2120 info:eu-repo/semantics/altIdentifier/arxiv/2506.11651 info:eu-repo/semantics/openAccess