2013 Fiscal Year Final Research Report
Basic research for renormalization group oriented stochastic analysis
| 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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| 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 |
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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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Research Products
(60 results)
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[Remarks] 集中講義 服部哲弥,「確率的順位付け」2011年7月, 京都大学 理学部 集中講義
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[Remarks] 論文誌編集南就将, RIMS Kokyuroku Bessatsu B27(2011)南就将, 数理解析研究所講究録1855確率論シンポジウム(2013)
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[Remarks] 研究会世話人責任者南就将, ランダム作用素のスペクトルと関連する話題 (Spectra of Random Operators and Related Topics) : 2013年12月5-7日, 京都大学2012年12月5-7日, 京都大学2011年12月1-3日, 京都大学2010年12月8-9日, 慶應義塾大学南就将, 確率論シンポジウム (Probability Symposium) 2012年12月18-21日, 京都大学数理解析研究所
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[Remarks] プレプリントN. Minami, Definition and self-adjointness of the stochastic Airy operator, arXiv : 1401.0853v1 (2014)
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[Remarks] K.Yasuda, On the order of divergence of the sum of p-adic-valued independent identically distributed random variables, Professor Sergio Albeverio's Special Issue on Arabian Journal of Mathematics (2014)
