2021/02/28 by W. Klein, N. Lubbers, Nicholas Lubbers +4
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Complex Systems and Time Series Analysis #Computer science #Critical exponent #Distribution (mathematics) #Lambda #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Mean field theory #Multiplicative function #Multiplicative noise #Phase transition #Physics #Quantum mechanics #Scaling #Statistical physics #Theoretical and Computational Physics #cond-mat.stat-mech #physics.soc-ph
paper · pdf · doi:10.1103/physreve.104.014151
published as Phys. Rev. E 104, 014151 (2021) · The paper is complemented by simulations of the GED model reported in Kang K. L. Liu,1 N. Lubbers, 1 W. Klein, J. Tobochnik, B. M. Boghosian, and Harvey Gould, "Simulation of a generalized asset exchange model with economic growth and wealth distribution."
arxiv created 2021/06/24 · openalex publication_date 2021/07/30 · arxiv updated 2021/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We develop a mean-field theory of the growth, exchange, and distribution (GED) model introduced by Liu et al. [K. K. L. Liu et al., preceding paper, Phys. Rev. E 104, 014150 (2021)10.1103/PhysRevE.104.014150] that accurately describes the phase transition in the limit that the number of agents N approaches infinity. The GED model is a generalization of the yard-sale model in which the additional wealth added by economic growth is nonuniformly distributed to the agents according to their wealth in a way determined by the parameter λ. The model is shown numerically to have a phase transition at λ=1 and be characterized by critical exponents and critical slowing down. Our mean-field treatment of the GED model correctly predicts the existence of the phase transition, a critical slowing down, and the values of the critical exponents and introduces an energy whose probability satisfies the Boltzmann distribution for λ<1, implying that the system is in thermodynamic equilibrium in the limit that N→∞. We show that the values of the critical exponents obtained by varying λ for a fixed value of N do not satisfy the usual scaling laws, but do satisfy scaling if a combination of parameters, which we refer to as the Ginzburg parameter, is much greater than one and is held constant. We discuss possible implications of our results for understanding economic systems and the subtle nature of the mean-field limit in systems with both additive and multiplicative noise.