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

article A short proof of a central limit theorem for the order of the giant component and k-core published yes Michael Anastos author 0b2a4358-bb35-11ec-b7b9-e3279b593dbb Joshua Erde author Mihyun Kang author Vincent Pfenninger author MaKw department Combinatorial Optimisation Problems on Sparse Random Graphs project 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. https://research-explorer.ista.ac.at/download/22752/22845/2026_BulletinLondonMathSoc_Anastos.pdf application/pdfno Wiley2026 eng Bulletin of the London Mathematical Society 0024-6093 1469-2120 2506.1165110.1112/blms.70464 588 M. Anastos, J. Erde, M. Kang, and V. Pfenninger, “A short proof of a central limit theorem for the order of the giant component and k-core,” Bulletin of the London Mathematical Society, vol. 58, no. 8. Wiley, 2026. Anastos M, Erde J, Kang M, Pfenninger V. 2026. A short proof of a central limit theorem for the order of the giant component and k-core. Bulletin of the London Mathematical Society. 58(8), e70464. 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. Bulletin of the London Mathematical Society. 2026;58(8). doi:<a href="https://doi.org/10.1112/blms.70464">10.1112/blms.70464</a> Anastos, M., Erde, J., Kang, M., & Pfenninger, V. (2026). A short proof of a central limit theorem for the order of the giant component and k-core. Bulletin of the London Mathematical Society. Wiley. <a href="https://doi.org/10.1112/blms.70464">https://doi.org/10.1112/blms.70464</a> Anastos, Michael, et al. “A Short Proof of a Central Limit Theorem for the Order of the Giant Component and K-Core.” Bulletin of the London Mathematical Society, vol. 58, no. 8, e70464, Wiley, 2026, doi:<a href="https://doi.org/10.1112/blms.70464">10.1112/blms.70464</a>. M. Anastos, J. Erde, M. Kang, V. Pfenninger, Bulletin of the London Mathematical Society 58 (2026). Anastos, Michael, Joshua Erde, Mihyun Kang, and Vincent Pfenninger. “A Short Proof of a Central Limit Theorem for the Order of the Giant Component and K-Core.” Bulletin of the London Mathematical Society. Wiley, 2026. <a href="https://doi.org/10.1112/blms.70464">https://doi.org/10.1112/blms.70464</a>. 227522026-08-23T22:01:47Z2026-09-07T13:56:17Z