{"has_accepted_license":"1","status":"public","project":[{"_id":"8f906bd2-16d5-11f0-9cad-e07be8aa9ac9","grant_number":"ESP3863424","name":"Combinatorial Optimisation Problems on Sparse Random Graphs"}],"OA_place":"publisher","department":[{"_id":"MaKw"}],"scopus_import":"1","doi":"10.1112/blms.70464","month":"08","OA_type":"hybrid","ddc":["510"],"file":[{"date_created":"2026-09-07T13:53:26Z","file_id":"22845","success":1,"access_level":"open_access","relation":"main_file","file_size":248641,"checksum":"b4b21f05c3fc62fde243a5ddd46cef49","creator":"dernst","content_type":"application/pdf","file_name":"2026_BulletinLondonMathSoc_Anastos.pdf","date_updated":"2026-09-07T13:53:26Z"}],"quality_controlled":"1","oa_version":"Published Version","intvolume":"        58","type":"journal_article","date_published":"2026-08-01T00:00:00Z","volume":58,"external_id":{"arxiv":["2506.11651"]},"language":[{"iso":"eng"}],"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 𝑘\r\n-core for sparse random graphs."}],"author":[{"id":"0b2a4358-bb35-11ec-b7b9-e3279b593dbb","first_name":"Michael","last_name":"Anastos","full_name":"Anastos, Michael"},{"last_name":"Erde","full_name":"Erde, Joshua","first_name":"Joshua"},{"last_name":"Kang","full_name":"Kang, Mihyun","first_name":"Mihyun"},{"first_name":"Vincent","full_name":"Pfenninger, Vincent","last_name":"Pfenninger"}],"title":"A short proof of a central limit theorem for the order of the giant component and k-core","publication":"Bulletin of the London Mathematical Society","publication_identifier":{"issn":["0024-6093"],"eissn":["1469-2120"]},"_id":"22752","year":"2026","publication_status":"published","article_processing_charge":"Yes (in subscription journal)","PlanS_conform":"1","day":"01","arxiv":1,"date_updated":"2026-09-07T13:56:17Z","mathsc":["05C80","60F05"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Wiley","date_created":"2026-08-23T22:01:47Z","fulldoi":"https://doi.org/10.1112/blms.70464","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.","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"supplementarymaterial":"no","researchdata_availability":"no","citation":{"short":"M. Anastos, J. Erde, M. Kang, V. Pfenninger, Bulletin of the London Mathematical Society 58 (2026).","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>.","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>.","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>","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."},"das_tickbox":"0","file_date_updated":"2026-09-07T13:53:26Z","article_number":"e70464","oa":1,"issue":"8","article_type":"original"}