Quasi-Static Variation of Power-Law and Log-Normal Distributions of Urban Population |
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| Authors: | Atushi Ishikawa Shouji Fujimoto Arturo Ramos Takayuki Mizuno |
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| Institution: | 1.Department of Economic Informatics, Kanazawa Gakuin University, Kanazawa 920-1392, Japan;2.Department of Economic Analysis, Universidad de Zaragoza, 50005 Zaragoza, Spain;3.National Institute of Informatics, Tokyo 101-8430, Japan;4.The Graduate University for Advanced Studies [SOKENDAI], Kanagawa 240-0193, Japan;5.Center for Advanced Research in Finance, The University of Tokyo, Tokyo 113-0033, Japan |
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| Abstract: | We analytically derived and confirmed by empirical data the following three relations from the quasi-time-reversal symmetry, Gibrat’s law, and the non-Gibrat’s property observed in the urban population data of France. The first is the relation between the time variation of the power law and the quasi-time-reversal symmetry in the large-scale range of a system that changes quasi-statically. The second is the relation between the time variation of the log-normal distribution and the quasi-time-reversal symmetry in the mid-scale range. The third is the relation among the parameters of log-normal distribution, non-Gibrat’s property, and quasi-time-reversal symmetry. |
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| Keywords: | urban population power law log-normal distribution Gibrat’ s law non-gibrat property quasi-time-reversal symmetry |
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