The asymptotic rank of adjacency matrices of weighted configuration models over arbitrary fields
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909721828524032 |
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| author | van der Hofstad, Remco Müller, Noela Zhu, Haodong |
| author_facet | van der Hofstad, Remco Müller, Noela Zhu, Haodong |
| contents | We study the asymptotic rank of adjacency matrices of a large class of edge-weighted configuration models. Here, the weight of a (multi-)edge can be any fixed non-zero element from an arbitrary field, as long as it is independent of the (multi-)graph. Our main result demonstrates that the asymptotic behavior of the normalized rank of the adjacency matrix neither depends on the fixed edge-weights, nor on which field they are chosen from. Our approach relies on a novel adaptation of the component exploration method of \cite{janson2009new}, which enables the application of combinatorial techniques from \cite{coja2022rank, HofMul25}. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_02813 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The asymptotic rank of adjacency matrices of weighted configuration models over arbitrary fields van der Hofstad, Remco Müller, Noela Zhu, Haodong Combinatorics Probability 05C80, 60B20, 94B05 We study the asymptotic rank of adjacency matrices of a large class of edge-weighted configuration models. Here, the weight of a (multi-)edge can be any fixed non-zero element from an arbitrary field, as long as it is independent of the (multi-)graph. Our main result demonstrates that the asymptotic behavior of the normalized rank of the adjacency matrix neither depends on the fixed edge-weights, nor on which field they are chosen from. Our approach relies on a novel adaptation of the component exploration method of \cite{janson2009new}, which enables the application of combinatorial techniques from \cite{coja2022rank, HofMul25}. |
| title | The asymptotic rank of adjacency matrices of weighted configuration models over arbitrary fields |
| topic | Combinatorics Probability 05C80, 60B20, 94B05 |
| url | https://arxiv.org/abs/2508.02813 |