Non-Gibrat's law in the middle scale region

Details Non-Gibrat's law in the middle scale region Non-Gibrat's law in the middle scale region

2008-09-18

arxiv.org/abs/0809.3060v1

Physics

Physics and Society

8 pages, 14 figures

Scientific paper

By using numerical simulation, we confirm that Takayasu--Sato--Takayasu (TST) model which leads Pareto's law satisfies the detailed balance under Gibrat's law. In the simulation, we take an exponential tent-shaped function as the growth rate distribution. We also numerically confirm the reflection law equivalent to the equation which gives the Pareto index $\mu$ in TST model. Moreover, we extend the model modifying the stochastic coefficient under a Non-Gibrat's law. In this model, the detailed balance is also numerically observed. The resultant pdf is power-law in the large scale Gibrat's law region, and is the log-normal distribution in the middle scale Non-Gibrat's one. These are accurately confirmed in the numerical simulation.

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