@article{22752,
  abstract     = {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.},
  author       = {Anastos, Michael and Erde, Joshua and Kang, Mihyun and Pfenninger, Vincent},
  issn         = {1469-2120},
  journal      = {Bulletin of the London Mathematical Society},
  number       = {8},
  publisher    = {Wiley},
  title        = {{A short proof of a central limit theorem for the order of the giant component and k-core}},
  doi          = {10.1112/blms.70464},
  volume       = {58},
  year         = {2026},
}