Non-Gibrat's law in the middle scale region
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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- Fujiwara, Yoshi & Di Guilmi, Corrado & Aoyama, Hideaki & Gallegati, Mauro & Souma, Wataru, 2004.
"Do Pareto–Zipf and Gibrat laws hold true? An analysis with European firms,"
Physica A: Statistical Mechanics and its Applications,
Elsevier, vol. 335(1), pages 197-216.
- Yoshi Fujiwara & Corrado Di Guilmi & Hideaki Aoyama & Mauro Gallegati & Wataru Souma, 2003. "Do Pareto-Zipf and Gibrat laws hold true? An analysis with European Firms," Papers cond-mat/0310061, arXiv.org, revised Nov 2003.
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