A Brunnian Theorem for Finite Families of Random Variables
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866929728909213696 |
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| author | Dugowson, Stéphane |
| author_facet | Dugowson, Stéphane |
| contents | In 2014, during a study on the connectivity structures of quantum entanglement, I specifically introduced the notion of ''the connectivity structure of a family of random variables'' -- a structure that expresses the dependency relations between the variables in question -- and I stated the following proposition, which can be described as Brunnian in reference to Hermann Brunn's work on links (1892) : "Every finite connectivity structure is that of a family of random variables". At the time, however, I neglected to write down the proof of this assertion, merely providing an intuitive idea of it. The purpose of this article is to present such a proof. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_16997 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Brunnian Theorem for Finite Families of Random Variables Dugowson, Stéphane General Topology Probability In 2014, during a study on the connectivity structures of quantum entanglement, I specifically introduced the notion of ''the connectivity structure of a family of random variables'' -- a structure that expresses the dependency relations between the variables in question -- and I stated the following proposition, which can be described as Brunnian in reference to Hermann Brunn's work on links (1892) : "Every finite connectivity structure is that of a family of random variables". At the time, however, I neglected to write down the proof of this assertion, merely providing an intuitive idea of it. The purpose of this article is to present such a proof. |
| title | A Brunnian Theorem for Finite Families of Random Variables |
| topic | General Topology Probability |
| url | https://arxiv.org/abs/2502.16997 |