The European Physical Journal Special Topics

, Volume 216, Issue 1, pp 3–20 | Cite as

Statistical universality and the method of Poissonian randomizations

  • Iddo EliazarEmail author


In this paper we demonstrate the remarkable effectiveness of Poissonian randomizations in the generation of statistical universality. We do so via a highly versatile spatio-statistical model in which points are randomly scattered, according to a Poisson process, across a general metric space. The points have general independent and identically distributed random physical characteristics. A probe is positioned in space, and is affected by the points. The effect of a given point on the probe is a function of the physical characteristic of the point and the distance of the point from the probe. We determine the classes of Poissonian randomizations – i.e., the spatial Poissonian scatterings of the points – that render the effects of the points invariant with respect to the physical characteristics of the points. These Poissonian randomizations have intrinsic power-law structures, yield statistical robustness, and generate universal statistics including Lévy distributions and extreme-value distributions. In effect, our results establish how “fractal” spatial geometries lead to statistical universality.


Poisson Process European Physical Journal Special Topic Race Model Poissonian Intensity Statistical Universality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© EDP Sciences and Springer 2013

Authors and Affiliations

  1. 1.Holon Institute of TechnologyHolonIsrael

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