dorsal/arxiv
View SchemaFluctuation scaling versus gap scaling
| Authors | Zoltan Eisler, Janos Kertesz |
|---|---|
| Categories | |
| ArXiv ID | physics/0703128 |
| URL | https://arxiv.org/abs/physics/0703128 |
Abstract
Fluctuation scaling is observed phenomenon from complex networks through finance to ecology. It means that the variance and the mean of a specific quantity are related as $\ev{\sigma^2|n}\propto \ev{n|A}^{2\alpha}$ with $1/2\geq \alpha \geq 1$ when a parameter $A$ (usually the system size) is varied. $A$ can be the strength of the node, the capitalization of the firm or the area of the habitat. On the other hand, quantities often obey gap scaling meaning that their density function depends on, say, the system size $A$ as $P(n|A) = n^{-1}F(n/A^{\Phi})$. This note describes that these two notions cannot coexist except when $\alpha = 1$. In this way one can empirically exclude the possibility of gap scaling in many complex systems including population dynamics, stock market fluctuations and Internet router traffic, where $\alpha < 1$.
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"abstract": "Fluctuation scaling is observed phenomenon from complex networks through\nfinance to ecology. It means that the variance and the mean of a specific\nquantity are related as $\\ev{\\sigma^2|n}\\propto \\ev{n|A}^{2\\alpha}$ with\n$1/2\\geq \\alpha \\geq 1$ when a parameter $A$ (usually the system size) is\nvaried. $A$ can be the strength of the node, the capitalization of the firm or\nthe area of the habitat. On the other hand, quantities often obey gap scaling\nmeaning that their density function depends on, say, the system size $A$ as\n$P(n|A) = n^{-1}F(n/A^{\\Phi})$. This note describes that these two notions\ncannot coexist except when $\\alpha = 1$. In this way one can empirically\nexclude the possibility of gap scaling in many complex systems including\npopulation dynamics, stock market fluctuations and Internet router traffic,\nwhere $\\alpha \u003c 1$.",
"arxiv_id": "physics/0703128",
"authors": [
"Zoltan Eisler",
"Janos Kertesz"
],
"categories": [
"physics.soc-ph",
"physics.bio-ph",
"q-bio.QM",
"q-fin.ST"
],
"title": "Fluctuation scaling versus gap scaling",
"url": "https://arxiv.org/abs/physics/0703128"
},
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