Abstract
In order to understand the characteristics common to distributions which have both fractal and non-fractal scale regions in a unified framework, we introduce the concept of a typical scale. We employ a model of 2d gravity modified by the R 2 term as a tool to understand such distributions through the typical scale. This model is obtained by adding an interaction term with a typical scale to a scale invariant system. A distribution derived in the model provides power law one in the large scale region, but Weibull-like one in the small scale region. As examples of distributions which have both fractal and non-fractal regions, we take those of personal income and citation number of scientific papers. We show that these distributions are fitted fairly well by the distribution curves derived analytically in the R 2 2d gravity model. As a result, we consider that the typical scale is a useful concept to understand various distributions observed in the real world in a unified way. We also point out that the R 2 2d gravity model provides us with an effective tool to read the typical scales of various distributions in a systematic way.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Physica A: Statistical Mechanics and its Applications
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
