2024/06/20 by Ankit Jha, Ion Nechita, Jha, Ankit Kumar +1
Decision Sciences · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Probability and Risk Models #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2406.14153
openalex publication_date 2024/06/20 · openalex created_date 2024/06/22 · openalex updated_date 2026/08/01
In this paper, we study random instances of the classical marginal problem. We encode the problem in a graph, where the vertices have assigned fixed binary probability distributions, and edges have assigned random bivariate distributions having the incident vertex distributions as marginals. We provide estimates on the probability that a joint distribution on the graph exists, having the bivariate edge distributions as marginals. Our study is motivated by Fine's theorem in quantum mechanics. We study in great detail the graphs corresponding to CHSH and Bell-Wigner scenarios providing rations of volumes between the local and non-signaling polytopes.