Random walks on finite groups and application to statistics
Project/Area Number |
21540002
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Algebra
|
Research Institution | Hokkaido University |
Principal Investigator |
|
Project Period (FY) |
2009 – 2011
|
Project Status |
Completed (Fiscal Year 2011)
|
Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
|
Keywords | 有限群上のランダムウォーク / マルコフ空間 / マッキー関手 / 分割表 / データセット / 一致率検定 / 正確確率公式 / 数理考古学 / 有限群の表現の応用 / 代数統計 / アファイン幾何の応用 / 精核確率公式 |
Research Abstract |
1. We studied random walks on finite groups by using representation theory of finite groups, especially evaluation of their convergency ratio. 2. Applying the result of 1, we show that a random walk on a symmetric group induces a random sampling of covergency tables. 3. Applying some methods of algebraic geometry, we studies a problem in metal archaeology (lead isotope method with mixture of leads). 2 and 3 look unrelated, but Markokv spaces (higher dimentional simplexes) appear in both fields. 4. We studied Burnside rings and Mackey functors on Markov spaces in representation theory.
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Report
(4 results)
Research Products
(27 results)