arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2102.01274cond-mat.stat-mechphysics.soc-ph
收藏

具有经济增长和财富分配的资产交换模型的平均场论

Mean-field theory of an asset exchange model with economic growth and wealth distribution

W. Klein, N. Lubbers, Kang K. L. Liu, T. Khouw, Harvey Gould

备注：
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."
发表信息：
Phys. Rev. E 104, 014151 (2021)
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

我们开发了一个平均场论的增长，交换和分布（GED）模型介绍康等。（前一篇论文），准确地描述了相变的限制，代理$N$的数量接近无穷大。GED模型是庭院-销售模型的推广，在该模型中，经济增长所增加的额外财富以由参数$λ$确定的方式根据其财富不均匀地分配给代理人。数值计算表明，该模型在$λ=1$有一个相变，其特征在于临界指数和临界慢化。我们的平均场处理的GED模型正确地预测相变的存在，临界慢化，临界指数的值，并引入了一个能量，其概率满足玻尔兹曼分布的$λ< 1$，这意味着该系统是在热力学平衡的极限，$N \to \infty$。我们表明，通过改变$λ$以获得固定值的$N$而获得的临界指数值不满足通常的标度律，但如果参数组合（我们称之为金斯伯格参数）远大于1并保持不变，则确实满足标度律。我们讨论了我们的研究结果可能产生的影响，了解经济系统和微妙的性质的平均场限制系统的加性和乘性噪声。

英文摘要：

We develop a mean-field theory of the growth, exchange and distribution (GED) model introduced by Kang et al. (preceding paper) 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 was 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, critical slowing down, 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 $N \to \infty$. 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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑