Abstract
Many random populations can be modeled as a countable set of points scattered randomly on the positive half-line. The points may represent magnitudes of earthquakes and tornados, masses of stars, market values of public companies, etc. In this article we explore a specific class of random such populations we coin ‘Paretian Poisson processes’. This class is elemental in statistical physics—connecting together, in a deep and fundamental way, diverse issues including: the Poisson distribution of the Law of Small Numbers; Paretian tail statistics; the Fréchet distribution of Extreme Value Theory; the one-sided Lévy distribution of the Central Limit Theorem; scale-invariance, renormalization and fractality; resilience to random perturbations.
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Eliazar, I., Klafter, J. Paretian Poisson Processes. J Stat Phys 131, 487–504 (2008). https://doi.org/10.1007/s10955-008-9505-3
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DOI: https://doi.org/10.1007/s10955-008-9505-3