A probabilistic treatise on the theory of orthogonal functions and random matrices
| Project/Area Number |
10640114
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Nagoya University |
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Principal Investigator |
CHIYONOBU Taizo Graduate School of Mathematics, Nagoya Univ., assistant, 大学院・多元数理科学研究科, 助手 (50197638)
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| Co-Investigator(Kenkyū-buntansha) |
SUGIURA Makoto Dept. of Mathematics, Ryukyu Univ., assistant professor, 理学部・数学教室, 助教授 (70252228)
AOMOTO Kazuhiko Graduate School of Mathematics, Nagoya Univ., Professor, 大学院・多元数理科学研究科, 教授 (00011495)
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| Project Period (FY) |
1998 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| Budget Amount *help |
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2000: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1999: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1998: ¥1,700,000 (Direct Cost: ¥1,700,000)
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| Keywords | limit theorem / random matrices |
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| Research Abstract |
T.Chiyonobu studied the probabilistic aspect of Szego's theorem, which plays the central role in the theory of the orthogonal functions and the random matrices. He pursued the new probabilistic proof of K Johansson's result, only to show more general result with the more regular potential instead of the logarithmic one.
K.Aomoto studied the Jacobi identity relateing the hypergeometric gunctions and the hyperplane arrangements. He also showed that the heat kernel associated with the Strum-Liouville operator with the logarithmic potential is given using the Wiener integral. That is, ina sense, the infinite dimensional version of the Gauss-Manin connection.
M.Sugiura studied the Ginzburg-Landau continuous Gibbs measure, and showed the spectral gap and the mixing property of the model.
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Report
(4 results)
Research Products
(14 results)
