Entropy dissipation and propagation of chaos for the uniform reshuffling model
Entropy dissipation and propagation of chaos for the uniform reshuffling model
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DOI：
10.1142/s0218202523500185
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发表时间：
2021-04
影响因子：
3.5
通讯作者：
Fei Cao;P. Jabin;Sébastien Motsch
中科院分区：
文献类型：
--
作者：
Fei Cao;P. Jabin;Sébastien Motsch
我们研究了货币交换的统一重新洗牌模型：两个随机选择的统一代理人在他们之间重新分配他们的美元。这种随机动态是平均场类型的，最终导致财富的指数分布。为了更好地理解这种动力学，我们研究了当代理数量达到无穷大时的极限。我们严格证明了所谓的混沌传播的随机动力学（限制）的非线性偏微分方程（PDE）。这种确定性的描述，这是众所周知的文献中，有味道的经典玻尔兹曼方程所产生的统计力学的稀释气体。在相对熵意义下，我们证明了它向指数平衡分布的收敛性。
We investigate the uniform reshuffling model for money exchanges: two agents picked uniformly at random redistribute their dollars between them. This stochastic dynamics is of mean-field type and eventually leads to a exponential distribution of wealth. To better understand this dynamics, we investigate its limit as the number of agents goes to infinity. We prove rigorously the so-called propagation of chaos which links the stochastic dynamics to a (limiting) nonlinear partial differential equation (PDE). This deterministic description, which is well-known in the literature, has a flavor of the classical Boltzmann equation arising from statistical mechanics of dilute gases. We prove its convergence toward its exponential equilibrium distribution in the sense of relative entropy.