  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.
