2015 Fiscal Year Final Research Report
Reconstruction of the theory of pont processes and Gibbs random fields and its application to equlibrium processes, fermion processes etc.
| Project/Area Number |
22540188
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | The University of Tokyo |
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Principal Investigator |
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| Project Period (FY) |
2010-04-01 – 2016-03-31
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| Keywords | 点過程(確率点場) / Gibbs測度 / 一般化Fock空間 / フェルミオン過程 / fermion(行列式)過程 / 平衡過程 / 大偏差原理 / カオスの伝播 |
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| Outline of Final Research Achievements |
A new general method to construct a Fock space representation associated with a given point process or random point field is introduced. It gives a simple description of important random fields such as equilibrium processes, Gibbs point fields, fermion(determinantal) processes and boson(permanental) processes.
In addition, the rapid mixing or cut-off phenomenon in Markov chains such as Ehrenfest model is shown to be a special case of the propagation of chaos (in the theory of Boltzmann equation), and which leads to a short proof without tedious computation.
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| Free Research Field |
確率解析・力学系、とくに統計力学と関連する数学的諸問題
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