2008/01/30 by Kim Christensen, Nadia Farid, Nazar Farid +2 · 2 citations
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1140/epjb/e2008-00173-2
6 pages, 2 figures, EPJB style
arxiv created 2008/01/30 · openalex publication_date 2008/04/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We derive general properties of the finite-size scaling of probability density functions and show that when the apparent exponent \tautilde of a probability density is less than 1, the associated finite-size scaling ansatz has a scaling exponent τequal 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 τ>=1 and τ>=\tautilde. Moreover, we show that if the scaling function G(x) approaches a non-zero constant for small arguments, limx-> 0 G(x) > 0, then τ=\tautilde. However, if the scaling function vanishes for small arguments, limx-> 0 G(x) = 0, then τ=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.