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...

Zipf’s law can be used to describe the rank-size distribution of cities in a region. It has seldom been employed to research urban internal structure. In this paper, we demonstrate that the space-filling process within a city follows Zipf’s law and can be characterized with the rank-size...

We present a statistical model for the distribution of Chinese names. Both family names and given names are studied on the same basis. With naive expectation, the distribution of family names can be very different from that of given names. One is affected mostly by genealogy, while the other can...

In this paper we report the existence of long-range memory in the opening moves of a chronologically ordered set of chess games using an extensive chess database. We used two mapping rules to build discrete time series and analyzed them using two methods for detecting long-range correlations;...

This paper formulates a random-growth urban model with a notion of geographical fitness. Using techniques of complex-network theory, we study our system as a type of preferential-attachment model with fitness, and we analyze its macro behavior to clarify the properties of the city-size...

We study the validity of Zipf’s Law in a data set of Chinese city sizes for the years 1999–2004, when the numbers of cities remain almost constant after a rapid urbanization process during the period of the market-oriented economy and reform-open policy. Previous investigations are...

We study the applicability of the q-exponential function for the distribution of family names. We mainly focus on the rank-size distribution of Japanese family names. The result supports the fact that the q-exponential distribution is relevant to the distribution of family names that is...

In this paper, we analyze statistical properties of English and Chinese written human language within the framework of weighted complex networks. The two language networks are based on an English novel and a Chinese biography, respectively, and both of the networks are constructed in the same...

Zipf’s power law is a general empirical regularity found in many systems. We report a detailed analysis of a burgeoning network of social groups, in which all ingredients needed for Zipf’s law to apply are verifiable and verified. A recently developed theory predicts that Zipf’s law...

We establish a “Central Limit Theorem” for rank distributions, which provides a detailed characterization and classification of their universal macroscopic statistics and phase transitions. The limit theorem is based on the statistical notion of Lorenz curves, and is termed the “Lorenzian...