How noise determines the statistics of simple path dependent systems

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Sample space reducing (SSR) processes offer a simple analytical understanding of the origin and ubiquity of scaling-laws in path-dependent complex systems. Assuming that noise is not uniformly strong within a system or across its life-span, but is state-dependent, SSR processes exhibit a wide range of statistical diversity beyond power-laws. We show that with simple state-dependent noise, SSR processes naturally yield Zipf’s law (no noise), power-laws (constant noise), log-normals (logarithmic noise), stretched exponentials (power-law noise), Gamma (linear noise), and many others.

B. Corominas-Murtra, R. Hanel, L. Zavojanni, S. Thurner, How noise determines the statistics of simple path dependent systems (in review)