Universality of random matrices and complex networks
| Project/Area Number |
25400397
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Nagoya University |
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Principal Investigator |
Nagao Taro 名古屋大学, 多元数理科学研究科, 教授 (10263196)
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| Research Collaborator |
TATE tatsuya
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| Project Period (FY) |
2013-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | ランダム行列 / 普遍性 / 複雑ネットワーク |
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| Outline of Final Research Achievements |
In complex network models, describing the connection pattern of networks such as the internet, the degree (the number of edges directly connecting to a vertex) has a property (scale-free property) to be distributed according to a power law. Mathematical models of networks with scale-free property were constructed, and the eigenvalue distributions of the adjacency matrices were studied. In addition, random matrix models with complex eigenvalues were extended and universal behavior was found, by using the property of orthogonal polynomials on the complex plane.
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| Academic Significance and Societal Importance of the Research Achievements |
ランダム行列理論は、サイズの大きい行列の固有値の分布に普遍的な振る舞いがあることを明らかにするものであるが、本研究では、これまで主に研究されてきた実固有値の分布の普遍性に加えて、複素固有値の分布の普遍性についての理解を深めることができた。また、ランダム行列理論の研究において開発されてきた手法は、数学や物理学の研究だけではなく、複雑ネットワークの記述を通じることにより、社会現象の研究にまで適用可能であることが示された。
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Report
(7 results)
Research Products
(17 results)
