Entropy dissipation and propagation of chaos for the uniform reshuffling model

Fei Cao, Pierre Emmanuel Jabin, Sebastien Motsch

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)829-875
Number of pages47
JournalMathematical Models and Methods in Applied Sciences
Volume33
Issue number4
DOIs
StatePublished - Apr 1 2023

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Applied Mathematics

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