Entropy dissipation and propagation of chaos for the uniform reshuffling model

Autor:	Cao, Fei, Jabin, Pierre-Emmanuel, Motsch, Sebastien
Rok vydání:	2021
Předmět:	Mathematics - Probability Mathematics - Analysis of PDEs 35A23 35Q91 82C31
Druh dokumentu:	Working Paper
Popis:	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. Comment: 48 pages, 8 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2104.01302 Zobrazit plný text záznamu View this record from Arxiv