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arXiv · 0809.3060

Non-Gibrat's law in the middle scale region

Masashi Tomoyose·Shouji Fujimoto·Atushi Ishikawa
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Abstract

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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Masashi Tomoyose, Shouji Fujimoto, Atushi Ishikawa. 2008-09-18. Non-Gibrat's law in the middle scale region. https://doi.org/10.1143/ptps.179.114

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