2013 Fiscal Year Final Research Report
Study on stochastic processes with determinantal structure
| Project/Area Number |
22340020
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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 | Kyushu University |
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Principal Investigator |
SHIRAI Tomoyuki 九州大学, マス・フォア・インダストリ研究所, 教授 (70302932)
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| Co-Investigator(Kenkyū-buntansha) |
TANEMURA Hideki 千葉大学, 大学院・理学系研究科, 教授 (40217162)
KATORI Makoto 中央大学, 理工学部, 教授 (60202016)
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| Co-Investigator(Renkei-kenkyūsha) |
OSADA Hirofumi 九州大学, 大学院・数理学研究院, 教授 (20177207)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | Ginibre 点過程 / 行列式点過程 / Palm 測度 / 絶対連続性 / 相関関数 / ランダム行列 / アルファ行列式 |
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| Research Abstract |
Correlation functions of the eigenvalues of certain random matrices can be expressed by using determinant. A point configuration whose correlation functions are determinants has repulsive property and is called a determinantal point process. Many mathematical objects can be described as a determinantal point process and analyzed precisely. We study the Ginibre point process, which is a typical model of determinantal point process, and we use this determinantal point process instead of poisson point process as a model of base stations of a cellular network and analyze it. We investigated determinantal point processes from both theoretical and applied mathematical points of view.
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