The process of fluctuations of the giant component of an Erdős-Rényi graph
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911755709448192 |
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| author | Enriquez, Nathanaël Faraud, Gabriel Lemaire, Sophie |
| author_facet | Enriquez, Nathanaël Faraud, Gabriel Lemaire, Sophie |
| contents | We present a detailed study of the evolution of the giant component of the Erdős-Rényi graph process as the mean degree increases from 1 to infinity. It leads to the identification of the limiting process of the rescaled fluctuations of its order around its deterministic asymptotic. This process is Gaussian with an explicit covariance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_07701 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The process of fluctuations of the giant component of an Erdős-Rényi graph Enriquez, Nathanaël Faraud, Gabriel Lemaire, Sophie Probability Combinatorics 05C80 (Primary) 60F17 (Secondary) We present a detailed study of the evolution of the giant component of the Erdős-Rényi graph process as the mean degree increases from 1 to infinity. It leads to the identification of the limiting process of the rescaled fluctuations of its order around its deterministic asymptotic. This process is Gaussian with an explicit covariance. |
| title | The process of fluctuations of the giant component of an Erdős-Rényi graph |
| topic | Probability Combinatorics 05C80 (Primary) 60F17 (Secondary) |
| url | https://arxiv.org/abs/2311.07701 |