论文标题
从相互作用的代理商到玻尔兹曼·吉布斯的货币分配
From interacting agents to Boltzmann-Gibbs distribution of money
论文作者
论文摘要
我们调查了货币交流的公正模型：代理商在彼此之间随机付出了一美元（如果有）。令人惊讶的是，这种动态最终导致了财富的几何分布（在[11]中由Dragulescu和Yakovenko经验显示，并严格地在[2,12,15,18]中表现出来）。我们证明，由于代理的数量进入无穷大，这将使混乱的统一传播产生，这将随机动力学与普通微分方程的确定性无限系统联系起来。然后，通过利用几种熵 - 内向耗散不等式来分析此确定性描述，并在相对熵中提供了趋于平衡（几何分布）的定量差异速率。
We investigate the unbiased model for money exchanges: agents give at random time a dollar to one another (if they have one). Surprisingly, this dynamics eventually leads to a geometric distribution of wealth (shown empirically by Dragulescu and Yakovenko in [11] and rigorously in [2,12,15,18]). We prove a uniform-in-time propagation of chaos result as the number of agents goes to infinity, which links the stochastic dynamics to a deterministic infinite system of ordinary differential equations. This deterministic description is then analyzed by taking advantage of several entropy-entropy dissipation inequalities and we provide a quantitative almost-exponential rate of convergence toward the equilibrium (geometric distribution) in relative entropy.
