2025/02/24 by Stéphane Dugowson, Dugowson, Stéphane
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #General Topology (math.GN) #Probability (math.PR) #Topological and Geometric Data Analysis #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2502.16997
openalex publication_date 2025/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.