2013 Fiscal Year Final Research Report
Discrete geometric analysis of the scaling limit and its applications
| Project/Area Number |
24840002
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
TANAKA Ryokichi 東北大学, 原子分子材料科学高等研究機構, 助教 (80629759)
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| Project Period (FY) |
2012-08-31 – 2014-03-31
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| Keywords | 大域解析学 / 離散幾何解析学 / ランダムウォーク / 離散群 / 等周定数 |
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| Research Abstract |
We studied the random walks on groups and the geometry of random graphs having their origins in statistical physics. Those are related to the central theme of this project. In particular, we focused on the important example in the three-dimensional solvable Lie groups and its discrete subgroups, and showed that the harmonic measure associated with the random walk drastically changes its measure-theoretic property according to the step distribution. We also studied the related problems arising from this subject.
Furthermore, we estimated the isoperimetric constant which has an important role in the geometry of the graphs for locally free product of random graphs.
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