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Generalised central limit theorems for growth rate distribution of complex systems. (English) Zbl 1291.91161

Summary: 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.

MSC:

91B62 Economic growth models
60F05 Central limit and other weak theorems
60K40 Other physical applications of random processes
62P20 Applications of statistics to economics
91B38 Production theory, theory of the firm

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