AUTHOR=Ishikawa Atushi , Fujimoto Shouji , Ramos Arturo , Mizuno Takayuki 

TITLE=Initial Value Dependence of Urban Population's Growth-Rate Distribution and the Long-Term Growth

JOURNAL=Frontiers in Physics

VOLUME=Volume 8 - 2020

YEAR=2020

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.00302

DOI=10.3389/fphy.2020.00302

ISSN=2296-424X

ABSTRACT=This paper uses the census information of the municipal population data of the United States, Italy, and Spain to analyze the statistical properties of their 10-year growth (short-term properties). We confirmed that the smaller the initial urban population is, the greater the probability that the urban population will decrease and that the probability that the urban population will increase does not depend on the initial urban population.
We also observed the statistical properties of the long-term growth of urban populations in each country over 100 years and specifically identified the following properties by observing the geometric mean of logarithmically equal-sized bins of the oldest urban population in the data used in the analysis. 1) The average urban population is increasing or decreasing exponentially with time.  2) The smaller the initial average urban population is, the smaller the exponent, which can be negative in Italy and Spain.  3) When the average urban population is large, exponential growth may stop. We showed that these long-term properties are derived from a short-term property by random sampling simulations from real data.