2013 Fiscal Year Final Research Report
Construction and Application of Statisitical Mechanics for Random Curves and Patterns
| Project/Area Number |
21540397
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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 |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Chuo University |
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Principal Investigator |
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| Project Period (FY) |
2009-04-01 – 2014-03-31
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| Keywords | 非平衡統計力学 / 確率過程 / 数理物理学 / ランダム行列 / ランダムパターン |
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| Research Abstract |
(1) We defined determinantal processes on spatio-temporal planes as generalizations of determinantal point processes.Using systems of multiple-orthogonal functions, we proved that the noncolliding Brownian motion and the noncolliding Bessel processes are determinantal processes for arbitrary initial configurations with finite numbers of particles, in which all spatio-temporal correlation functions of these processes are determined. We constructed nonequilibrium systems with an infinite number of particles and studied relaxation phenomena to equilibrium states.
(2) We introduced a new notion, a complex Brownian motion representation, for the noncolliding Brownian motion. If the system has this representation, we can prove that it is determinantal and all spatio-temporal correlation functions are obtained.
(3) We studied O'Connell process, which is related with the quantum Toda lattice. We formulated this proces as a generalization of the noncolliding Brownian motion.
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