TY - JOUR

T1 - Entropy dissipation and propagation of chaos for the uniform reshuffling model

AU - Cao, Fei

AU - Jabin, Pierre Emmanuel

AU - Motsch, Sebastien

N1 - Funding Information:
We would like to thank the anonymous reviewer for the careful reading of our paper and the many insightful comments and suggestions. S. Motsch would like to acknowledge support from the National Science Foundation, DMS-2206330. P.E.J. was partially supported by NSF DMS Grants DMS-2049020, DMS-2205694 and DMS-2219397.
Publisher Copyright:
© World Scientific Publishing Company.

PY - 2023/4/1

Y1 - 2023/4/1

N2 - 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.

AB - 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.

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U2 - 10.1142/S0218202523500185

DO - 10.1142/S0218202523500185

M3 - Article

AN - SCOPUS:85150716046

SN - 0218-2025

VL - 33

SP - 829

EP - 875

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

IS - 4

ER -