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