Large deviations of the giant component in scale-free inhomogeneous random graphs
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909236154335232 |
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| author | Jorritsma, Joost Zwart, Bert |
| author_facet | Jorritsma, Joost Zwart, Bert |
| contents | We study large deviations of the size of the largest connected component in a general class of inhomogeneous random graphs with iid weights, parametrized so that the degree distribution is regularly varying. We derive a large-deviation principle with logarithmic speed: the rare event that the largest component contains linearly more vertices than expected is caused by the presence of constantly many vertices with linear degree. Conditionally on this rare event, we prove distributional limits of the weight distribution and component-size distribution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01224 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large deviations of the giant component in scale-free inhomogeneous random graphs Jorritsma, Joost Zwart, Bert Probability 05C80, 60F10 We study large deviations of the size of the largest connected component in a general class of inhomogeneous random graphs with iid weights, parametrized so that the degree distribution is regularly varying. We derive a large-deviation principle with logarithmic speed: the rare event that the largest component contains linearly more vertices than expected is caused by the presence of constantly many vertices with linear degree. Conditionally on this rare event, we prove distributional limits of the weight distribution and component-size distribution. |
| title | Large deviations of the giant component in scale-free inhomogeneous random graphs |
| topic | Probability 05C80, 60F10 |
| url | https://arxiv.org/abs/2407.01224 |