Study of inequalities and variational principle in free probability theory
| Project/Area Number |
21540208
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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 |
Global analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
HIAI Fumio 東北大学, 大学院・情報科学研究科, 名誉教授 (30092571)
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| Co-Investigator(Renkei-kenkyūsha) |
UEDA Yoshimichi 九州大学, 大学院・数理学研究院, 准教授 (00314724)
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| Project Period (FY) |
2009 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 関数解析学 / 作用素 / 行列解析 / 量子情報 / 自由確率論 / 行列 / 量子確率 / 確率論 / 作用素環 / 作用素論 / 量子確率論 / 量子情報理論 / ランダム行列 |
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| Research Abstract |
In the course of this research project we obtained various results in the three subjects of free probability, quantum probability and operator/matrix analysis. We studied free probability theory related to free entropy and free Fisher information. In quantum probability and quantum information, our study was directed to quantum relative entropy, quantum hypothesis testing and monotone Riemannian metrics. Several results in matrix analysis were also obtained concerning operator monotone and convex functions, matrix trace and norm functions, operator means and symmetric (anti) norms, etc.
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Report
(5 results)
Research Products
(65 results)
