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# Directed Random Market: the equilibrium distribution

Listed:
• Guy Katriel

## Abstract

We find the explicit expression for the equilibrium wealth distribution of the Directed Random Market process, recently introduced by Mart\'inez-Mart\'inez and L\'opez-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.

## Suggested Citation

• Guy Katriel, 2014. "Directed Random Market: the equilibrium distribution," Papers 1404.4068, arXiv.org.
• Handle: RePEc:arx:papers:1404.4068
as

File URL: http://arxiv.org/pdf/1404.4068

## References listed on IDEAS

as
1. Angle, John, 2006. "The Inequality Process as a wealth maximizing process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 388-414.
2. Mukherjea, A. & Rao, M. & Suen, S., 2006. "A note on moment generating functions," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1185-1189, June.
3. Adrian Dragulescu & Victor M. Yakovenko, 2000. "Statistical mechanics of money," Papers cond-mat/0001432, arXiv.org, revised Aug 2000.
4. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518, arXiv.org, revised Dec 2009.
Full references (including those not matched with items on IDEAS)

## Citations

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Cited by:

1. Guy Katriel, 2014. "The Immediate Exchange model: an analytical investigation," Papers 1409.6646, arXiv.org.

### NEP fields

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