Central limit theorems for Soft random simplicial complexes
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915384299356160 |
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| author | Candela, Julián David |
| author_facet | Candela, Julián David |
| contents | A soft random graph $G(n,r,p)$ can be obtained from the random geometric graph $G(n,r)$ by keeping every edge in $G(n,r)$ with probability $p$. The soft random simplicial complexes is a model for random simplicial complexes built over the soft random graph $G(n,r,p)$. This new model depends on a probability vector $ρ$ which allows the simplicial complexes to present randomness in all dimensions. In this article, we use a normal approximation theorem to prove central limit theorems for the number of $k$-faces and for the Euler's characteristic for soft random simplicial complexes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_10625 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Central limit theorems for Soft random simplicial complexes Candela, Julián David Probability Algebraic Topology A soft random graph $G(n,r,p)$ can be obtained from the random geometric graph $G(n,r)$ by keeping every edge in $G(n,r)$ with probability $p$. The soft random simplicial complexes is a model for random simplicial complexes built over the soft random graph $G(n,r,p)$. This new model depends on a probability vector $ρ$ which allows the simplicial complexes to present randomness in all dimensions. In this article, we use a normal approximation theorem to prove central limit theorems for the number of $k$-faces and for the Euler's characteristic for soft random simplicial complexes. |
| title | Central limit theorems for Soft random simplicial complexes |
| topic | Probability Algebraic Topology |
| url | https://arxiv.org/abs/2311.10625 |