Quantitative convergence guarantees for the mean-field dispersion process

Abstract

We study the discrete Fokker-Planck equation associated with the mean-field dynamics of a particle system called the dispersion process. For different regimes of the average number of particles per site (denoted by $\mu >0$), we establish various quantitative long-time convergence guarantees toward the global equilibrium (depending on the sign of $\mu -1$), which is also confirmed by numerical simulations. The main novelty/contribution of this manuscript lies in the careful and tricky analysis of a nonlinear Volterra-type integral equation satisfied by a key auxiliary function.

33 pages, 7 figures

References in corpus (10)

• Statistical mechanics of money
• Statistical mechanics of money: How saving propensity affects its distribution
• Pareto Law in a Kinetic Model of Market with Random Saving Propensity
• An $H$ theorem for Boltzmann's equation for the Yard-Sale Model of asset exchange
• Kinetic models of immediate exchange
• Quantitative propagation of chaos for generalized Kac particle systems
• Rigorous proof of the Boltzmann-Gibbs distribution of money on connected graphs
• Rigorous results for the distribution of money on connected graphs (models with debts)
• Uniform propagation of chaos for a dollar exchange econophysics model
• Dispersion on the Complete Graph