| Project/Area Number |
20340025
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
OBATA Nobuaki 東北大学, 大学院・情報科学研究科, 教授 (10169360)
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| Co-Investigator(Kenkyū-buntansha) |
HIAI Fumio 東北大学, 大学院・情報科学研究科, 教授 (30092571)
URAKAWA Hajime 東北大学, 国際教育院, 教授 (50022679)
SUZUKI Kanako 東北大学, 国際高等研究教育機構, 助教 (10451519)
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| Co-Investigator(Renkei-kenkyūsha) |
LIANG Song 筑波大学, 大学院・数理物質科学研究科, 准教授 (60324399)
HORA Akihito 名古屋大学, 多元数理科学研究科, 教授 (10212200)
SAITO Kimiaki 名城大学, 理工学部, 教授 (90195983)
HOROSHIMA Fumio 九州大学, 大学院・数理学研究院, 准教授 (00330358)
YOSHIDA Hiroaki お茶の水女子大学, 大学院・人間文化創成科学研究科, 教授 (10220667)
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥12,350,000 (Direct Cost: ¥9,500,000、Indirect Cost: ¥2,850,000)
Fiscal Year 2010: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2009: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2008: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
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| Keywords | 量子確率論 / ホワイトノイズ解析 / 無限次元解析 / 複雑ネットワーク / 直交多項式 / 確率解析 / フーリエ-ガウス変換 / 量子中心極限定理 / フーリエ・ガウス変換 |
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| Research Abstract |
We investigated mathematical models of random phenomena by revealing and utilizing non-commutative structures hidden behind. We introduced the new concept of quantum white noise derivative and applied to generalization of quantum stochastic integrals, integral representation of Fock space operators, representation of quantum martingales, and characterization of Bogoliubov transformation. For the structural analysis of complex networks, we developed the quantum probabilistic approach to spectral analysis and transition probability of random walks, and studied free probability, free entropy, and matrix inequalities.
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