Directed Random Market: the equilibrium distribution

Abstract

We find the explicit expression for the equilibrium wealth distribution of the Directed Random Market process, recently introduced by Martínez-Martínez and López-Ruiz, which turns out to be a Gamma distribution with shape parameter $\frac{1}{2}$. We also prove the convergence of the discrete-time process describing the evolution of the distribution of wealth to the equilibrium distribution.

References in corpus (1)

• Colloquium: Statistical mechanics of money, wealth, and income

Cited by in corpus (1)

• Clausius inequality and H-theorems for some models of random wealth exchange