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The urban system and its diversity are essential resources for economic development. At the intra-regional level, cities that do not have the status of the regional administrative centre shape the structure and diversity of the urban system. The article presents the results of the study on the distribution of non-capital Russian cities (depending on their size) as well as on the mobility patterns that influence their dynamics in the post-Soviet period. Based on data about the population of the Russian cities in the period 1991 — 2016, the study uses the method for analysing the dynamics of the distribution with the application of Markov chains. The study has demonstrated the predominance of downward mobility of non-capital cities within the city size distribution, which results in their considerable concentration at the left side of the distribution and the decrease in the diversity of city size. Simultaneously, the mobility of cities is more intense in the eastern part of the country, as the mobility patterns contribute to the preservation of greater diversity of city size (compared to the western part). It is possible to identify three groups of non-capital cities that differ in mobility patterns and distribution directions. Th e fir st gro up includ es cities belonging to agglomerations of large regional capitals, whose dynamics of distribution are opposite to the dynamics of the distribution of the totality of non-capital cities. The second group comprises cities belonging to the agglomeration shadow with the most unfavourable dynamics of the distribution. The third group contains remote cities located in the periphery, which show a slight tendency towards the formation of a bimodal distribution. The scale of these groups differs in the eastern and western parts of Russia. The findings complement the results of other studies, expand knowledge about the modern dynamics of regional settlement systems, as well as determine further research areas. The revealed negative trends in the evolution of the city size distribution substantiate the need for a transition to the regulated development of the urban system. Such an approach should consider the consequences of the spatial development policy for different groups of cities and should strive to maintain the diversity of settlement systems.

The evolution of city size distribution in China has gained a great deal of scholarly attention. However, little is known about the effect of economic transition on the reorganization of city size distribution in China. Using an urban hierarchy with cascade structure model, we decompose Zipf’s law into two exponential functions that provide a new way of examining the dynamic processes of urban system evolution. This study aims to investigate the dominating latent forces that affect China’s city size distribution through mathematical modeling of the hierarchical scaling laws based on census data of 1982, 1990, 2000, and 2010. A number of features of China’s city size distribution are found. First, the size distribution of Chinese cities displayed a clear trend of evolving toward the Zipf distribution, which is the result of economic transition from planned to market. Second, the rank-size pattern still deviates slightly from the standard Zipf distribution, as indicated by the narrow scaling range and departure of the scaling exponent from the theoretically expected value. We argue that the top-down state regulation is a critical cause of deviation of China’s city size distribution from Zipf’s law.

In this paper we study Zipf’s law, which postulates that the product of a city’s population and its rank (the number of cities with a larger or equal population) is constant for every city in a given region. We show that the empirical literature indicates that the law may not always hold, although its general form, the rank-size rule, could be a good first approximation of city size distribution. We perform our own empirical analysis of the distribution of the population of Polish cities on the largest possible sample to find that Zipf’s law is rejected for Poland as the city sizes are less evenly distributed than it predicts.

This paper uses un-truncated city population data from six countries (the United States, Spain, Italy, France, England and Japan) to illustrate how parametric growth regressions can lead to biased results when testing for Gibrat’s law in city size distributions. The OLS results show non-monotonic behaviours depending on the sample size. Moreover, it is possible to find a critical sample size from which we reject Gibrat’s law.

This paper discusses the size distribution, - in economic terms - of the Italian municipalities over the period 2007-2011. Yearly data are rather well fitted by a modified Lavalette law, while Zipf-Mandelbrot-Pareto law seems to fail in this doing. The analysis is performed either at a national as well as at a local (regional and provincial) level. Deviations are discussed as originating in so called king and vice-roy effects. Results confirm that Italy is shared among very different regional realities. The case of Lazio is puzzling., Comment: 34 pages; 49 references; 29 figures; 9 Tables; to be published in Physica A

The aim of this work is to test empirically the validity of Gibrat’s law on the growth of cities, using data on the complete distribution of cities (without size restrictions) from three countries (the US, Spain and Italy) for the entire 20th century. In order to achieve this, different techniques are used. First, panel data unit root tests tend to confirm the validity of Gibrat’s law in the upper-tail distribution. Secondly, when the entire distribution is considered using non-parametric methods, it is found that Gibrat’s law does not hold exactly in the long term (in general, size affects the variance of the growth process but not its mean). Moreover, the log-normal distribution works well as a description of city size distributions across the whole century when no truncation point is considered.