Continuum and thermodynamic limits for a simple random-exchange model

During, Bertram, Georgiou, Nicos, Merino-Aceituno, Sara and Scalas, Enrico (2022) Continuum and thermodynamic limits for a simple random-exchange model. Stochastic Processes and their Applications, 149. pp. 248-277. ISSN 0304-4149

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Abstract

We discuss various limits of a simple random exchange model that can be used for the distribution of wealth. We start from a discrete state space - discrete time version of this model and, under suitable scaling, we show its functional convergence to a continuous space - discrete time model. Then, we show a thermodynamic limit of the empirical distribution to the solution of a kinetic equation of Boltzmann type. We solve this equation and we show that the solutions coincide with the appropriate limits of the invariant measure for the Markov chain. In this way we complete Boltzmann’s program of deriving kinetic equations from random dynamics for this simple model. Three families of invariant measures for the mean field limit are discovered and we show that only two of those families can be obtained as limits of the discrete system while the third is extraneous.

Item Type: Article
Keywords: Wealth distribution, Mean-field limits, Functional limits, Markov chains, Kinetic equations, Partitions of integers
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
SWORD Depositor: Mx Elements Account
Depositing User: Mx Elements Account
Date Deposited: 13 Apr 2022 09:21
Last Modified: 22 Apr 2022 10:15
URI: http://sro.sussex.ac.uk/id/eprint/105321

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