The local weak limit of $k$-dimensional hypertrees
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2021
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910627666067456 |
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| author | Mészáros, András |
| author_facet | Mészáros, András |
| contents | Let $\mathcal{C}(n,k)$ be the set of $k$-dimensional simplicial complexes $C$ over a fixed set of $n$ vertices such that:
(1) $C$ has a complete $k-1$-skeleton;
(2) $C$ has precisely ${{n-1}\choose {k}}$ $k$-faces;
(3) the homology group $H_{k-1}(C)$ is finite.
Consider the probability measure on $\mathcal{C}(n,k)$ where the probability of a simplicial complex $C$ is proportional to $|H_{k-1}(C)|^2$. For any fixed $k$, we determine the local weak limit of these random simplicial complexes as $n$ tends to infinity.
This local weak limit turns out to be the same as the local weak limit of the $1$-out $k$-complexes investigated by Linial and Peled. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_11504 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The local weak limit of $k$-dimensional hypertrees Mészáros, András Combinatorics Probability Let $\mathcal{C}(n,k)$ be the set of $k$-dimensional simplicial complexes $C$ over a fixed set of $n$ vertices such that: (1) $C$ has a complete $k-1$-skeleton; (2) $C$ has precisely ${{n-1}\choose {k}}$ $k$-faces; (3) the homology group $H_{k-1}(C)$ is finite. Consider the probability measure on $\mathcal{C}(n,k)$ where the probability of a simplicial complex $C$ is proportional to $|H_{k-1}(C)|^2$. For any fixed $k$, we determine the local weak limit of these random simplicial complexes as $n$ tends to infinity. This local weak limit turns out to be the same as the local weak limit of the $1$-out $k$-complexes investigated by Linial and Peled. |
| title | The local weak limit of $k$-dimensional hypertrees |
| topic | Combinatorics Probability |
| url | https://arxiv.org/abs/2101.11504 |