Fluctuation scaling in complex systems: Taylor's law and beyond

By Zoltán Eisler, Imre Bartos, János Kertész. 2007

314 citations recorded by the source corpus.

Complex systems consist of many interacting elements which participate in some dynamical process. The activity of various elements is often different and the fluctuation in the activity of an element grows monotonically with the average activity. This relationship is often of the form ‘fluctuations ≈ constant × averageα’, where the exponent α is predominantly in the range [1/2, 1]. This power law has been observed in a very wide range of disciplines, ranging from population dynamics through the Internet to the stock market and it is often treated under the names Taylor's law or fluctuation scaling. This review attempts to show how general the above scaling relationship is by surveying the literature, as well as by reporting some new empirical data and model calculations. We also show some basic principles that can underlie the generality of the phenomenon. This is followed by a mean-field framework based on sums of random variables. In this context the emergence of fluctuation scaling is equivalent to some corresponding limit theorems. In certain physical systems fluctuation scaling can be related to finite size scaling. 1Dedicated to the memory of L. R. Taylor (1924–2007).

Subfields: Economics and Econometrics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/74de46cde0423522cee770371b7bda2b225facd5

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Citations in the corpus

Inflammatory markers in depression: A meta-analysis of mean differences and variability in 5,166 patients and 5,083 controls (2020, unknown): “Given that most cytokines are increased in depression, and variance often scales with mean (Eisler et al., 2008), differences in relative variability may, at least partially, be a function of between-group differences in”
Scaling laws of human interaction activity (2009, result): “Similar correlation results have been found in traded values of stocks and e-mail data (22).”