论文标题
从二项式改组模型到金钱的泊松分布
From the binomial reshuffling model to Poisson distribution of money
论文作者
论文摘要
我们提出了一种新颖的改组交换模型，并研究了其长期行为。在此型号中，通过翻转一系列公平硬币，将两个人$ x_i $和$ x_j $随机挑选，他们的财富被重新分配，导致二项式发行$ b \ circ（x_i+x_j）$。这种动力学可以被认为是生态植物学中所谓的均匀改组模型的自然变体[2,14]。随着个体的数量进入无穷大，我们得出了其平均场极限，这将随机动力学与普通微分方程的确定性无限系统联系起来。然后，这项工作的主要结果是证明（使用耦合论证）证明财富的分布收敛于$ 2 $ - Wasserstein Metric的泊松分布。数值模拟说明了主要结果，并表明多项式收敛衰减可能会进一步改善。
We present a novel reshuffling exchange model and investigate its long time behavior. In this model, two individuals are picked randomly, and their wealth $X_i$ and $X_j$ are redistributed by flipping a sequence of fair coins leading to a binomial distribution denoted $B \circ (X_i+X_j)$. This dynamics can be considered as a natural variant of the so-called uniform reshuffling model in econophysics [2,14]. As the number of individuals goes to infinity, we derive its mean-field limit, which links the stochastic dynamics to a deterministic infinite system of ordinary differential equations. The main result of this work is then to prove (using a coupling argument) that the distribution of wealth converges to the Poisson distribution in the $2$-Wasserstein metric. Numerical simulations illustrate the main result and suggest that the polynomial convergence decay might be further improved.
