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On the scaling of probability density functions with apparent power-law exponents less than unity
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Christensen, Kim, Farid, Nadia, Pruessner, Gunnar and Stapleton, M. (2008) On the scaling of probability density functions with apparent power-law exponents less than unity. European Physical Journal B. Condensed Matter and Complex Systems, Vol.62 (No.3). pp. 331-336. doi:10.1140/epjb/e2008-00173-2 ISSN 1434-6028.
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Official URL: http://dx.doi.org/10.1140/epjb/e2008-00173-2
Abstract
We derive general properties of the finite-size scaling of probability density functions and show that when the apparent exponent ($) over tilde of a probability density is less than 1, the associated finite-size scaling ansatz has a scaling exponent center dot equal to 1, provided that the fraction of events in the universal scaling part of the probability density function is non-vanishing in the thermodynamic limit. We find the general result that center dot >= 1 and center dot >= (center dot) over tilde. Moreover, we show that if the scaling function G(center dot) approaches a non-zero constant for small arguments, lim(x -> 0) G(center dot) center dot 0, then center dot = (center dot) over tilde. However, if the scaling function vanishes for small arguments, lim(x -> 0) G(center dot) = 0, then center dot = 1, again assuming a non-vanishing fraction of universal events. Finally, we apply the formalism developed to examples from the literature, including some where misunderstandings of the theory of scaling have led to erroneous conclusions.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QC Physics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Scaling laws (Statistical physics), System theory, Self-organizing systems, Critical phenomena (Physics), Critical point, Density functionals | ||||
Journal or Publication Title: | European Physical Journal B. Condensed Matter and Complex Systems | ||||
Publisher: | Springer | ||||
ISSN: | 1434-6028 | ||||
Official Date: | April 2008 | ||||
Dates: |
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Volume: | Vol.62 | ||||
Number: | No.3 | ||||
Number of Pages: | 6 | ||||
Page Range: | pp. 331-336 | ||||
DOI: | 10.1140/epjb/e2008-00173-2 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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