2013/12/25 by Ted Theodosopoulos, Theodosopoulos, Ted
Economics, Econometrics and Finance · Physics and Astronomy · #60K37 #91B69 #91B80 #Complex Systems and Time Series Analysis #FOS: Mathematics #Opinion Dynamics and Social Influence #Probability (math.PR) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1312.7025
openalex publication_date 2013/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a new type of spin market model, populated by hierarchical agents, represented as configurations of sites and arcs in an evolving network. We describe two analytic techniques for investigating the asymptotic behavior of this model: one based on the spectral theory of Markov chains and another exploiting contingent submartingales to construct a deterministic cellular automaton that approximates the stochastic dynamics. Our study of this system documents a phase transition between a sub-critical and a super-critical regime based on the values of a coupling constant that modulates the tradeoff between local majority and global minority forces. In conclusion, we offer a speculative socioeconomic interpretation of the resulting distributional properties of the system.