Fluctuations of the giant of Poisson random graphs
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915088094461952 |
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| author | Clancy Jr, David |
| author_facet | Clancy Jr, David |
| contents | Enriquez, Faraud, and Lemaire (2023) have established process-level fluctuations for the giant of the dynamic Erdős-Rényi random graph above criticality and show that the limit is a centered Gaussian process with continuous sample paths. A random walk proof was recently obtained by Corujo, Limic and Lemaire (2024). We show that a similar result holds for rank-one inhomogeneous models whenever the empirical weight distribution converges to a limit and its second moment converges as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01354 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fluctuations of the giant of Poisson random graphs Clancy Jr, David Probability 60F17, 05C80 Enriquez, Faraud, and Lemaire (2023) have established process-level fluctuations for the giant of the dynamic Erdős-Rényi random graph above criticality and show that the limit is a centered Gaussian process with continuous sample paths. A random walk proof was recently obtained by Corujo, Limic and Lemaire (2024). We show that a similar result holds for rank-one inhomogeneous models whenever the empirical weight distribution converges to a limit and its second moment converges as well. |
| title | Fluctuations of the giant of Poisson random graphs |
| topic | Probability 60F17, 05C80 |
| url | https://arxiv.org/abs/2501.01354 |