Eigenvalue Distribution of Large Weighted Random Sparse Uniform $q$-Hypergraphs
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915450247446528 |
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| author | Vengerovsky, Valentin |
| author_facet | Vengerovsky, Valentin |
| contents | We study eigenvalue distribution of the adjacency matrix $A^{(N,p,q)}$ of weighted random uniform $q$-hypergraphs $Γ= Γ_{N,p,q}$. We assume that the graphs have $N$ vertices and the average number of hyperedges attached to one vertex is $(q-1)!\cdot p$. To each edge of the graph $e_{ij}$ we assign a weight given by a random variable $a_{ij}$ with all moments finite. We consider the moments of normalized eigenvalue counting function $σ_{N,p,q}$ of $A^{(N,p,q)}$. Assuming all moments of $a$ finite, we obtain recurrent relations that determine the moments of the limiting measure $σ_{p,q} = \lim_{N\to\infty} σ_{N,p,q}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13297 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Eigenvalue Distribution of Large Weighted Random Sparse Uniform $q$-Hypergraphs Vengerovsky, Valentin Combinatorics Mathematical Physics 60B20, 15B52 We study eigenvalue distribution of the adjacency matrix $A^{(N,p,q)}$ of weighted random uniform $q$-hypergraphs $Γ= Γ_{N,p,q}$. We assume that the graphs have $N$ vertices and the average number of hyperedges attached to one vertex is $(q-1)!\cdot p$. To each edge of the graph $e_{ij}$ we assign a weight given by a random variable $a_{ij}$ with all moments finite. We consider the moments of normalized eigenvalue counting function $σ_{N,p,q}$ of $A^{(N,p,q)}$. Assuming all moments of $a$ finite, we obtain recurrent relations that determine the moments of the limiting measure $σ_{p,q} = \lim_{N\to\infty} σ_{N,p,q}$. |
| title | Eigenvalue Distribution of Large Weighted Random Sparse Uniform $q$-Hypergraphs |
| topic | Combinatorics Mathematical Physics 60B20, 15B52 |
| url | https://arxiv.org/abs/2508.13297 |