 Power laws in cities population, financial markets and internet sites (scaling in systems with a variable number of components)Aharon Blank and Sorin Solomon Physica A: Statistical Mechanics and its Applications, 2000, vol. 287, issue 1, 279-288 Abstract: We study a few dynamical systems composed of many components whose sizes evolve according to multiplicative stochastic rules. We compare them with respect to the emergence of power laws in the size distribution of their components. We show that the details specifying and enforcing the smallest size of the components are crucial as well as the rules for creating new components. In particular, a growing system with a fixed number of components and a fixed smallest component size does not converge to a power law. We present a new model with variable number of components that converges to a power law for a very wide range of parameters. In a very large subset of this range, one obtains for the exponent α the special value 1 specific for the city populations distribution. We discuss the conditions in which α can take different values. In the case of the stock market, the distribution of the investors’ wealth is related to the ratio between the new capital invested in stock and the rate of increase of the stock index. Date: 2000 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:287:y:2000:i:1:p:279-288 DOI: 10.1016/S0378-4371(00)00464-7 Access Statistics for this article Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis More articles in Physica A: Statistical Mechanics and its Applications from Elsevier |
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