中尺度区域的非Gibrat定律
Non-Gibrat's law in the middle scale region
摘要：
通过数值模拟，我们证实了在Gibrat定律下，引导Pareto定律的Takayasu-Sato-Takayasu（TST）模型满足细致平衡。在模拟中，我们采用指数帐篷形函数作为增长率分布。我们还用数值方法证实了反射定律与TST模型中给出Pareto指数$μ$的方程是等价的。此外，我们扩展了模型修改的随机系数下的非Gibrat的法律。在该模型中，还观察到了细致平衡。在大尺度Gibrat定律区域，其概率密度服从幂律分布，在中等尺度Non-Gibrat定律区域，其概率密度服从对数正态分布。这些都在数值模拟中得到了准确的证实。
英文摘要：
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 $μ$ 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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