2011 Fiscal Year Final Research Report
Infinite-dimensional stochastic dynamical systems motivated by random matrices and statistical physics
| Project/Area Number |
21340031
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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 |
Basic analysis
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| Research Institution | Kyushu University |
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Principal Investigator |
OSADA Hirofumi 九州大学, 大学院・数理学研究院, 教授 (20177207)
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| Co-Investigator(Kenkyū-buntansha) |
FUNAKI Tadahisa 東京大学, 大学院・数理科学研究科, 教授 (60112174)
TANEMURA Hideki 千葉大学, 大学院・理学研究科, 教授 (40217162)
SHIRAI Tomoyuki 九州大学, 大学院・数理学研究院, 教授 (70302932)
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| Co-Investigator(Renkei-kenkyūsha) |
KATORI Makoto 中央大学, 理工学部, 教授 (60202016)
OTOBE Yoshiki 信州大学, 理学部, 准教授 (30334882)
SHINODA Masato 奈良女子大学, 理学部, 准教授 (50271044)
YANO Yuko 京都大学, 大学院・理学研究科, 助教 (10337462)
YANO Kouji 京都大学, 大学院・理学研究科, 准教授 (80467646)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 確率解析 / 対数ガス / クーロンポテンシャル / 無限次元確率力学系 / ランダム行列 / 干渉ブラウン運動 / 点過程 / 拡散過程 |
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| Research Abstract |
We have established a general construction theorem and an SDE representation theorem for interacting Brownian motions with 2D Coulomb potentials. We have applied them to the representative random point fields arising from Random Matrix Theory such as Ginibre, Dyson, Bessel random point fields, and have detected and solve the infinite-dimensional stochastic differential equations describing the associated stochastic dynamics. We prove the Palm measures of Ginibre random point field have very strange property that is very different from usual Gibbs measures with Ruelle' s class interaction potentials. We have constructed the time evolutional model of 2D Young diagram and have proved its scaling limit.
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