A short proof of a central limit theorem for the order of the giant component and k-core
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.
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Author
Anastos, MichaelISTA;
Erde, Joshua;
Kang, Mihyun;
Pfenninger, Vincent
Department
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.
Publishing Year
Date Published
2026-08-01
Journal Title
Bulletin of the London Mathematical Society
Publisher
Wiley
Acknowledgement
This research was funded in whole or in part by the Austrian Science Fund (FWF) [10.55776/P36131 (Joshua Erde), 10.55776/I6502 (Mihyun Kang), 10.55776/ESP3863424 (Michael Anastos)] and by the Swiss National Science Foundation (SNSF) [P500-2_235474] (Vincent Pfenninger). For open access purposes, the authors have applied a CC BY public copyright license to any author accepted manuscript version arising from this submission. The authors thank the reviewers for helpful comments on the paper, and for bringing the particular form of Theorem 2.2 to our attention.
Volume
58
Issue
8
Article Number
e70464
ISSN
eISSN
IST-REx-ID
Cite this
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:10.1112/blms.70464
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. https://doi.org/10.1112/blms.70464
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. https://doi.org/10.1112/blms.70464.
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, 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:10.1112/blms.70464.
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