A short proof of a central limit theorem for the order of the giant component and $k$-core
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912428526141440 |
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| author | Anastos, Michael Erde, Joshua Kang, Mihyun Pfenninger, Vincent |
| author_facet | Anastos, Michael Erde, Joshua Kang, Mihyun Pfenninger, Vincent |
| contents | In this note we outline a new and simple approach to proving central limit theorems for various 'global' graph parameters which 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11651 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A short proof of a central limit theorem for the order of the giant component and $k$-core Anastos, Michael Erde, Joshua Kang, Mihyun Pfenninger, Vincent Combinatorics Probability 05C80, 60F05 In this note we outline a new and simple approach to proving central limit theorems for various 'global' graph parameters which 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. |
| title | A short proof of a central limit theorem for the order of the giant component and $k$-core |
| topic | Combinatorics Probability 05C80, 60F05 |
| url | https://arxiv.org/abs/2506.11651 |