Star-collision in random hypergraphs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909049696550912 |
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| author | Adhikari, Kartick Parui, Samiron |
| author_facet | Adhikari, Kartick Parui, Samiron |
| contents | We study star-based symmetries in uniform hypergraphs and their consequences for matrices whose entries depend only on vertex stars. Such matrices admit a deterministic decomposition into a global component and a local component supported on equivalence classes of vertices with identical stars, known as units. While nontrivial units may exist at finite size in hypergraphs of uniformity greater than two, their persistence in random settings has remained unclear.
We analyze star collisions in random $k$-uniform hypergraphs and show that, in some particular regimes, nontrivial units disappear with high probability as the number of vertices grows. As a consequence, star-dependent matrices exhibit asymptotically trivial local structure, and their spectral behavior, invariant subspaces, and associated linear dynamics are governed by a reduced quotient object obtained by contracting vertex stars.
These results identify star collisions as a finite-size phenomenon in random hypergraphs and clarify the asymptotic irrelevance of star-based symmetries for operator behavior in large random systems in particular regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16856 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Star-collision in random hypergraphs Adhikari, Kartick Parui, Samiron Combinatorics Probability 05C65, 05C80, 05C50 We study star-based symmetries in uniform hypergraphs and their consequences for matrices whose entries depend only on vertex stars. Such matrices admit a deterministic decomposition into a global component and a local component supported on equivalence classes of vertices with identical stars, known as units. While nontrivial units may exist at finite size in hypergraphs of uniformity greater than two, their persistence in random settings has remained unclear. We analyze star collisions in random $k$-uniform hypergraphs and show that, in some particular regimes, nontrivial units disappear with high probability as the number of vertices grows. As a consequence, star-dependent matrices exhibit asymptotically trivial local structure, and their spectral behavior, invariant subspaces, and associated linear dynamics are governed by a reduced quotient object obtained by contracting vertex stars. These results identify star collisions as a finite-size phenomenon in random hypergraphs and clarify the asymptotic irrelevance of star-based symmetries for operator behavior in large random systems in particular regimes. |
| title | Star-collision in random hypergraphs |
| topic | Combinatorics Probability 05C65, 05C80, 05C50 |
| url | https://arxiv.org/abs/2605.16856 |