2011 Fiscal Year Final Research Report
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
|
| 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 |
|---|
| 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.
|
-
-
-
-
-
-
-
-
-
-
-
-
-
-
[Remarks] 以下は大学院生・研究者向けの談話会での講演.本研究のテーマと関係している
-
[Remarks] (2012近大)吉田知行「代数と組み合わせ論をカテゴリー化しよう」,於『近畿大学理工学部数学談話会』,近畿大学,2012/03/02
-
[Remarks] (2011熊本)吉田知行「代数統計ことはじめ」,於『熊本大学談話会』,熊本大学,2011/06/24
-
[Remarks] (2010山形)吉田知行「代数統計ことはじめ」,於『山形大学談話会』,山形大学,2010/11/11
