dorsal/arxiv
View SchemaPower-law behavior and condensation phenomena in disordered urn models
| Authors | Jun-ichi Inoue, Jun Ohkubo |
|---|---|
| Categories | |
| ArXiv ID | physics/0606068 |
| URL | https://arxiv.org/abs/physics/0606068 |
Abstract
We investigate equilibrium statistical properties of urn models with disorder. Two urn models are proposed; one belongs to the Ehrenfest class, and the other corresponds to the Monkey class. These models are introduced from the view point of the power-law behavior and randomness; it is clarified that quenched random parameters play an important role in generating power-law behavior. We evaluate the occupation probability $P(k)$ with which an urn has $k$ balls by using the concept of statistical physics of disordered systems. In the disordered urn model belonging to the Monkey class, we find that above critical density $\rho_\mathrm{c}$ for a given temperature, condensation phenomenon occurs and the occupation probability changes its scaling behavior from an exponential-law to a heavy tailed power-law in large $k$ regime. We also discuss an interpretation of our results for explaining of macro-economy, in particular, emergence of wealth differentials.
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"abstract": "We investigate equilibrium statistical properties of urn models with\ndisorder. Two urn models are proposed; one belongs to the Ehrenfest class, and\nthe other corresponds to the Monkey class. These models are introduced from the\nview point of the power-law behavior and randomness; it is clarified that\nquenched random parameters play an important role in generating power-law\nbehavior. We evaluate the occupation probability $P(k)$ with which an urn has\n$k$ balls by using the concept of statistical physics of disordered systems. In\nthe disordered urn model belonging to the Monkey class, we find that above\ncritical density $\\rho_\\mathrm{c}$ for a given temperature, condensation\nphenomenon occurs and the occupation probability changes its scaling behavior\nfrom an exponential-law to a heavy tailed power-law in large $k$ regime. We\nalso discuss an interpretation of our results for explaining of macro-economy,\nin particular, emergence of wealth differentials.",
"arxiv_id": "physics/0606068",
"authors": [
"Jun-ichi Inoue",
"Jun Ohkubo"
],
"categories": [
"physics.soc-ph",
"physics.data-an"
],
"title": "Power-law behavior and condensation phenomena in disordered urn models",
"url": "https://arxiv.org/abs/physics/0606068"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "41b9422b-0e48-41a7-ae51-f4ececb3fa67",
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