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Keywords
(8)
Critical Phenomena
Finite Size Scaling
Probability Density
Probability Density Function
Scale Function
Scaling Exponent
Thermodynamic Limit
Power Law
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On the scaling of probability density functions with apparentpowerlaw exponents less than unity
On the scaling of probability density functions with apparentpowerlaw exponents less than unity,10.1140/epjb/e2008001732,European Physical Journal
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On the scaling of probability density functions with apparentpowerlaw exponents less than unity
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Kim Christensen
,
Nadia Farid
,
Gunnar Pruessner
,
Matthew Stapleton
. We derive general properties of the finitesize scaling of
probability density
functions and show that when the apparent exponent of a
probability density
is less than 1, the associated finitesize scaling ansatz has a
scaling exponent
τ equal to 1, provided that the fraction of events in the universal scaling part of the
probability density function
is nonvanishing in the thermodynamic limit. We find the general result that τ≥1 and . Moreover, we show that if the scaling function approaches a nonzero constant for small arguments, 0$" align="middle" border="0"> , then . However, if the scaling function vanishes for small arguments, , then τ= 1, again assuming a nonvanishing 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.
Journal:
European Physical Journal B  EUR PHYS J B
, vol. 62, no. 3, pp. 331336, 2008
DOI:
10.1140/epjb/e2008001732
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