2016 Fiscal Year Final Research Report
Representation theory, random matrices, and related topics
| Project/Area Number |
25800062
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Kagoshima University (2014-2016)
Nagoya University (2013) |
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Principal Investigator |
Matsumoto Sho 鹿児島大学, 理工学域理学系, 准教授 (60547553)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Keywords | 確率論 / 表現論 / 組合せ論 |
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| Outline of Final Research Achievements |
We have developed Weingarten calculus, which is a method for computing mixed moments of matrix elements from various random matrices. Specifically, we construct Weingarten calculus for random matrices associated with seven kinds of compact symmetric spaces, inverses of compound Wishart matrices, and pseudo-inverses of Ginibre matrices. Furthermore, we obtain a new inequality for traces from circular beta-ensembles by using Jack polynomials, and show the central limit theorem as its application. Also, we find a polynomiality of Plancherel averages.
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| Free Research Field |
確率論
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