# Regensburg 2019 – wissenschaftliches Programm

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# SOE: Fachverband Physik sozio-ökonomischer Systeme

## SOE 12: Poster

### SOE 12.8: Poster

### Dienstag, 2. April 2019, 16:00–19:00, Poster A

**Continuous increases or decreases in city sizes observed in Japanese telephone directory data** — •Takaaki Ohnishi^{1}, Takayuki Mizuno^{2}, and Tsutomu Watanabe^{1} — ^{1}The University of Tokyo, Tokyo, Japan — ^{2}National Institute of Informatics, Tokyo, Japan

In order to investigate urban development and decline, we empirically study the number of shops and facilities *x*(*t*) at municipality level in Japan observed in fixed-line telephone directory data from 2011 to 2017. Observation of the scatter plot for *x*(*t*) and the annual growth rates *r*(*t*)=log(*x*(*t*+1)/*x*(*t*)) supports that *r*(*t*) decrease with its size *x*(*t*). Both Kendall rank correlation coefficient and Pearson correlation coefficient show significant negative correlation between them, indicating deviations from Gibrat’s law. This result is similar to what is found for population growth. There is significant positive correlation between two successive annual growth rates *r*(*t*) and *r*(*t*+1), implying that cities with large (small) *r*(*t*) tend to be larger (smaller) in the next year. Then, we evaluate the conditional probability of size increase (decrease) in the next size change after *n* successive size increase (decrease) and find that the probability is significantly larger than 0.5. As *n* becomes larger, the probability gradually increases. Probabilities of successive negative size changes are slightly higher than that of positive size changes. We observe these properties even for each industry as well as for each prefecture. These findings suggest that city sizes are more likely to continue increasing or decreasing, which help to characterize urban dynamics.