Discrete-time integrable systems and partition functions of vicious walk systems
| Project/Area Number |
22740063
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kyoto University |
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Principal Investigator |
KAMIOKA Shuhei 京都大学, 大学院・情報学研究科, 助教 (70543297)
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| Project Period (FY) |
2010 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 統計数学 / 組合せ論 / 可積分系 / 非衝突ランダムウォーク / 直交多項式 / 連分数 / タイリング / vicious walk / 非交叉径路 / Aztec diamond / 行列式 / Gessel-Viennotの補題 / 非交叉経路 / グラフ / パデ近似 / 超離散可積分系 |
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| Research Abstract |
Vicious walk systems are multiparticle systems in which every two particles, or walkers, cannot occupy the same site at the same time. In this research we consider vicious walk systems on lattice graphs of various types, including the square and triangular lattices. In particular, focusing on the calculation of partition functions, we construct lattice graphs on which we can find a closed form of partition functions. To do that, we utilize discrete-time integrable systems having determinant solutions such as the discrete hungry Toda equation. Applications to ultradiscrete integrable systems as well as combinatorial problems are also considered.
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Report
(3 results)
Research Products
(18 results)
