| Project/Area Number |
18540125
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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 | Kochi University |
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Principal Investigator |
NAKANO Fumihiko Kochi University, 教育研究部自然科学系, 准教授 (10291246)
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| Co-Investigator(Kenkyū-buntansha) |
南 就将 慶応大学, 医学部, 教授 (10183964)
上木 直昌 京都大学, 大学院・人間・環境学研究科, 准教授 (80211069)
加藤 和久 高知大学, 理学部, 教授 (20036578)
諸澤 俊介 高知大学, 理学部, 教授 (50220108)
小松 和志 高知大学, 理学部, 准教授 (00253336)
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| Co-Investigator(Renkei-kenkyūsha) |
MINAMI Nariyuki 慶応大学, 医学部, 教授 (10183964)
UEKI Naomasa 京都大学, 人間環境学科, 准教授 (80211069)
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| Project Period (FY) |
2006 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥3,430,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥630,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2006: ¥700,000 (Direct Cost: ¥700,000)
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| Keywords | ランダムシュレーディンガー作用素 / アンダーソン局在 / 局在中心 / アンダーソンモデル / 点過程 / ランダム磁場 / 無限分解可能点過程 / 確率論 / ベーテ格子 / ランダム測度 |
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| Research Abstract |
We consider the distribution of eigenvalue and eigenfunction on the localized region of the random Schroednger operator on d-dimensional square lattice. We showed that, (1) they are uniformly distributed, as a whole, (2) they obey Poisson distribution in the natural scaling limit, and (3) they are repulsive under smaller scaling. Moreover, if we have Minami's estimate, the same results also hold for the random Schrodeinger operaors on the continuum.
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