Generalised central limit theorems for growth rate distribution of complex systems

TL;DR

This paper presents a solvable model for the growth rate distribution of complex systems with many independent subunits, deriving scaling relations and distributions that match empirical data from business firms.

Contribution

It introduces a theoretical model that explains various observed growth rate distributions and scaling properties in complex systems, supported by real-world data analysis.

Findings

Scaling relations are consistent with the model.

Growth rate distribution has a power-law tail.

Empirical data from business firms fit the theoretical distribution.

Abstract

We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling properties and distributions reported for growth rates of complex systems in a variety of fields can be derived from this basic physical model. Statistical data of growth rates for about 1 million business firms are analysed as a real-world example of randomly growing systems. Not only are the scaling relations consistent with the theoretical solution, but the entire functional form of the growth rate distribution is fitted with a theoretical distribution that has a power-law tail.