Stretched exponentials from superstatistics

Christian Beck

Physica A: Statistical Mechanics and its Applications, 2006, vol. 365, issue 1, 96-101

Abstract: Distributions exhibiting fat tails occur frequently in many different areas of science. A dynamical reason for fat tails can be a so-called superstatistics, where one has a superposition of local Gaussians whose variance fluctuates on a rather large spatio-temporal scale. After briefly reviewing this concept, we explore in more detail a class of superstatistics that hasn’t been subject of many investigations so far, namely superstatistics for which a suitable power βη of the local inverse temperature β is χ2-distributed. We show that η>0 leads to power-law distributions, while η<0 leads to stretched exponentials. The special case η=1 corresponds to Tsallis statistics and the special case η=-1 to exponential statistics of the square root of energy. Possible applications for granular media and hydrodynamic turbulence are discussed.

Keywords: Fluctuating temperature; Superstatistics; Fat tails (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (10)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:365:y:2006:i:1:p:96-101

DOI: 10.1016/j.physa.2006.01.030

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Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

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