Why Does Zipf's Law Break Down in Rank-Size Distribution of Cities?(Cross-disciplinary physics and related areas of science and technology)

We study the rank-size distribution of cities in Japan by data analysis and computer simulation. From the census data after World War II, we find that the rank-size distribution of cities is composed of two parts, each of which has an independent power exponent. In addition, the power exponent of the head part of the distribution changes with time and Zipf's law holds only for a restricted period. We show that Zipf's law broke down owing to the great Showa and Heisei mergers and recovered owing to population growth in middle-sized cities after the great Showa merger.

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