Paretian poisson processes

Iddo Eliazar*, Joseph Klafter

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)487-504
Number of pages18
JournalJournal of Statistical Physics
Issue number3
StatePublished - May 2008


  • Fractals
  • Probability theory
  • Statistics
  • Stochastic processes


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