Universal self-similarity of propagating populations

Iddo Eliazar, Joseph Klafter

Research output: Contribution to journalArticlepeer-review

Abstract

This paper explores the universal self-similarity of propagating populations. The following general propagation model is considered: particles are randomly emitted from the origin of a d -dimensional Euclidean space and propagate randomly and independently of each other in space; all particles share a statistically common-yet arbitrary-motion pattern; each particle has its own random propagation parameters-emission epoch, motion frequency, and motion amplitude. The universally self-similar statistics of the particles' displacements and first passage times (FPTs) are analyzed: statistics which are invariant with respect to the details of the displacement and FPT measurements and with respect to the particles' underlying motion pattern. Analysis concludes that the universally self-similar statistics are governed by Poisson processes with power-law intensities and by the Fréchet and Weibull extreme-value laws.

Original languageEnglish
Article number011112
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume82
Issue number1
DOIs
StatePublished - 12 Jul 2010

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