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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.03516 |
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| _version_ | 1866908631158489088 |
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| author | Backhausz, Ágnes Kuehn, Christian van der Niet, Sjoerd Zucal, Giulio |
| author_facet | Backhausz, Ágnes Kuehn, Christian van der Niet, Sjoerd Zucal, Giulio |
| contents | In this work, we develop a spectral theory for hypergraph limits. We prove the convergence of the spectra of adjacency and Laplacian matrices for hypergraph sequences converging in the $1$-cut metric. On the other hand, we give examples of matrix operators associated with hypergraphs whose spectra are not continuous with respect to the $1$-cut metric. Furthermore, we show that these operators are continuous with respect to other cut norms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03516 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral theory of dense hypergraph limits Backhausz, Ágnes Kuehn, Christian van der Niet, Sjoerd Zucal, Giulio Combinatorics Spectral Theory 05C65, 37A30 In this work, we develop a spectral theory for hypergraph limits. We prove the convergence of the spectra of adjacency and Laplacian matrices for hypergraph sequences converging in the $1$-cut metric. On the other hand, we give examples of matrix operators associated with hypergraphs whose spectra are not continuous with respect to the $1$-cut metric. Furthermore, we show that these operators are continuous with respect to other cut norms. |
| title | Spectral theory of dense hypergraph limits |
| topic | Combinatorics Spectral Theory 05C65, 37A30 |
| url | https://arxiv.org/abs/2511.03516 |