Project/Area Number  10640114 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
General mathematics (including Probability theory/Statistical mathematics)

Research Institution  Nagoya University 
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)

CoInvestigator(Kenkyūbuntansha) 
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)

Project Fiscal Year 
1998 – 2000

Project Status 
Completed(Fiscal Year 2000)

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)

Keywords  limit theorem / random matrices / 極限定理 / ランダム行列 
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 StrumLiouville operator with the logarithmic potential is given using the Wiener integral. That is, ina sense, the infinite dimensional version of the GaussManin connection. M.Sugiura studied the GinzburgLandau continuous Gibbs measure, and showed the spectral gap and the mixing property of the model.
