Universal generation of statistical self-similarity: A randomized central limit theorem

Iddo Eliazar*, Joseph Klafter

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A universal mechanism for the generation of statistical self-similarity-i.e., fractality in the context of random processes-is established. We consider a generic system which superimposes independent stochastic signals, producing a system output; all signals share a common statistical signal pattern, yet each signal has its own transmission parameters-amplitude, frequency, and initiation epoch. We characterize the class of parameter randomizations yielding statistically self-similar outputs in a universal fashion-i.e., for whatever signals fed into the system. Statistically self-similar outputs with finite variance further display (i)anomalous diffusion behavior-characterized by power-law temporal variance growth-and (ii)1/f noise behavior-characterized by power-law power spectra. The mechanism presented is a "randomized central limit theorem" for fractal statistics of random processes.

Original languageEnglish
Article number040602
JournalPhysical Review Letters
Issue number4
StatePublished - 6 Aug 2009


Dive into the research topics of 'Universal generation of statistical self-similarity: A randomized central limit theorem'. Together they form a unique fingerprint.

Cite this