2022/02/08 by Victor Gitton, Gitton, Victor
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Methodology (stat.ME) #Opinion Dynamics and Social Influence #Quantum Physics (quant-ph) #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2202.04103
openalex publication_date 2022/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a framework, named the postselected inflation framework, to obtain converging outer approximations of the sets of probability distributions that are compatible with classical multi-network scenarios. Here, a network is a bilayer directed acyclic graph with a layer of sources of classical randomness, a layer of agents, and edges specifying the connectivity between the agents and the sources. A multi-network scenario is a list of such networks, together with a specification of subsets of agents using the same strategy. An outer approximation of the set of multi-network correlations provides means to certify the infeasibility of a list of agent outcome distributions. We furthermore show that the postselected inflation framework is mathematically equivalent to the standard inflation framework: in that respect, our results allow to gain further insights into the convergence proof of the inflation hierarchy of Navascuès and Wolfe [arXiv:1707.06476], and extend it to the case of multi-network scenarios.