Logarithmic typical distances in preferential attachment models
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912229860835328 |
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| author | van der Hofstad, Remco Zhu, Haodong |
| author_facet | van der Hofstad, Remco Zhu, Haodong |
| contents | We prove that the typical distances in a preferential attachment model with out-degree $m\geq 2$ and strictly positive fitness parameter are close to $\log_ν{n}$, where $ν$ is the exponential growth parameter of the local limit of the preferential attachment model. The proof relies on a path-counting technique, the first- and second-moment methods, as well as a novel proof of the convergence of the spectral radius of the offspring operator under a certain truncation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_07961 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Logarithmic typical distances in preferential attachment models van der Hofstad, Remco Zhu, Haodong Probability 05C80, 05C12, 05C82 We prove that the typical distances in a preferential attachment model with out-degree $m\geq 2$ and strictly positive fitness parameter are close to $\log_ν{n}$, where $ν$ is the exponential growth parameter of the local limit of the preferential attachment model. The proof relies on a path-counting technique, the first- and second-moment methods, as well as a novel proof of the convergence of the spectral radius of the offspring operator under a certain truncation. |
| title | Logarithmic typical distances in preferential attachment models |
| topic | Probability 05C80, 05C12, 05C82 |
| url | https://arxiv.org/abs/2502.07961 |