| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
Stochastic properties of non-equilibrium statistical mechanics models are described by spatio-temporal correlation functions. Non-colliding diffusive particle systems are known as the special cases in which all spatio-temporal correlation functions are given by determinants controlled by correlation kernels. The purpose of the present study is to clarify the mathematical structure of such exactly solvable non-equilibrium models called determinantal processes (DP). We have established a new notion of determinantal martingale representation (DMR). In probability theory a martingale is the general name of processes describing time evolutionary fluctuations. We have proved that if a system has DMR, then it is DP. This theorem reveals a new relationship between fluctuation and correlation in no-equilibrium. Using this new framework, we have reported elliptic-functional extensions of the systems and interesting relationship between DPs and plasma models as well as Gaussian free fields.
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