| Project/Area Number |
21340020
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Keio University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
MINAMI Nariyuki 慶應義塾大学, 医学部, 教授 (10183964)
YASUDA Kumi 慶應義塾大学, 商学部, 教授 (40284484)
ATSUJI Jun 慶應義塾大学, 経済学部, 教授 (00221044)
HATTORI Kumiko 首都大学, 東京・理工学研究科, 教授 (80231520)
TAKEDA Masayoshi 東北大学, 大学院・理学研究科, 教授 (30179650)
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| Co-Investigator(Renkei-kenkyūsha) |
SUZUKI Yuki 慶應義塾大学, 医学部, 専任講師 (30286645)
HARIYA Yuu 東北大学, 大学院・理学研究科, 准教授 (20404030)
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| Project Period (FY) |
2009-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥16,770,000 (Direct Cost: ¥12,900,000、Indirect Cost: ¥3,870,000)
Fiscal Year 2013: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2012: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2011: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2010: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2009: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
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| Keywords | 数理科学 / 確率過程論 / 粒子系 / 流体力学極限 / 確率順位付け模型 / ポワッソン過程 / 準線形偏微分方程式系 / 先頭に跳ぶ規則 / オンラインリテール / ロングテール / 無限粒子系 / 流体力学的極限 / ポワッソン確率過程 / Burgers方程式 / move-to-front規則 / 液体力学極限 / 確率ランキング模型 / くりこみ群 |
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| Research Abstract |
We defined a class of stochastic ranking models, which mathematically models the rankings found on the web, e.g., as sales ranks of online bookstores, and proved existence of hydrodynamic limits and propagation of chaos. The result has implications on the analysis of so called long-tail structure of online retails. The results are reported in the book `Solving the mystery of Amazon ranking' (in Japanese), as well as in scientific papers for journals on mathematics.
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