---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '22752'
abstract:
- lang: eng
  text: "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 \U0001D458\r\n-core for sparse random graphs."
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.
article_number: e70464
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Michael
  full_name: Anastos, Michael
  id: 0b2a4358-bb35-11ec-b7b9-e3279b593dbb
  last_name: Anastos
- first_name: Joshua
  full_name: Erde, Joshua
  last_name: Erde
- first_name: Mihyun
  full_name: Kang, Mihyun
  last_name: Kang
- first_name: Vincent
  full_name: Pfenninger, Vincent
  last_name: Pfenninger
citation:
  ama: 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>
  apa: Anastos, M., Erde, J., Kang, M., &#38; Pfenninger, V. (2026). 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>. Wiley. <a href="https://doi.org/10.1112/blms.70464">https://doi.org/10.1112/blms.70464</a>
  chicago: 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.” <i>Bulletin of the London Mathematical Society</i>. Wiley, 2026. <a href="https://doi.org/10.1112/blms.70464">https://doi.org/10.1112/blms.70464</a>.
  ieee: 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,” <i>Bulletin of
    the London Mathematical Society</i>, vol. 58, no. 8. Wiley, 2026.
  ista: 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.
  mla: Anastos, Michael, et al. “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>, vol. 58, no. 8, e70464, Wiley, 2026, doi:<a href="https://doi.org/10.1112/blms.70464">10.1112/blms.70464</a>.
  short: M. Anastos, J. Erde, M. Kang, V. Pfenninger, Bulletin of the London Mathematical
    Society 58 (2026).
das_tickbox: '0'
date_created: 2026-08-23T22:01:47Z
date_published: 2026-08-01T00:00:00Z
date_updated: 2026-09-07T13:56:17Z
day: '01'
ddc:
- '510'
department:
- _id: MaKw
doi: 10.1112/blms.70464
external_id:
  arxiv:
  - '2506.11651'
file:
- access_level: open_access
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  creator: dernst
  date_created: 2026-09-07T13:53:26Z
  date_updated: 2026-09-07T13:53:26Z
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fulldoi: https://doi.org/10.1112/blms.70464
has_accepted_license: '1'
intvolume: '        58'
issue: '8'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
mathsc:
- 05C80
- 60F05
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 8f906bd2-16d5-11f0-9cad-e07be8aa9ac9
  grant_number: ESP3863424
  name: Combinatorial Optimisation Problems on Sparse Random Graphs
publication: Bulletin of the London Mathematical Society
publication_identifier:
  eissn:
  - 1469-2120
  issn:
  - 0024-6093
publication_status: published
publisher: Wiley
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: A short proof of a central limit theorem for the order of the giant component
  and k-core
tmp:
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  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 58
year: '2026'
...