2005 Fiscal Year Final Research Report Summary
PROBLEMS ON THE HYDRODYNAMIC LIMIT AND RELATED TOPICS
| Project/Area Number |
15540109
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
UCHIYAMA Kohei Tokyo Institute of Technology, Mathematics, Professor, 大学院・理工学研究科, 教授 (00117566)
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| Co-Investigator(Kenkyū-buntansha) |
MURATA Minoru Tokyou Institute of Technology, Mathematics, Professor, 大学院・理工学研究科, 教授 (50087079)
IGUCHI Tatuo Tokyou Institute of Technology, Mathematics, Assoc.Professor, 大学院・理工学研究科, 助教授 (20294879)
HAMANA Yuji Kumamoto University, Mathematics, Professor, 理学部, 教授 (00243923)
HANDA Kenji Saga University, Mathematics, Assoc.Professor, 理工学部, 助教授 (10238214)
TANEMURA Hideki Chiba University, Mathematics, Professor, 理学部, 教授 (40217162)
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| Project Period (FY) |
2003 – 2005
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| Keywords | hydrodynamic limit / spectral gap / non-gradient system / principle of large deviations / fluctuation process |
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| Research Abstract |
In 2003 introducing a lattice gas model, called zero-range-exclusion model, which possesses two conservative quantities, we obtained an estimate of the spectral gap for the model [cf. An estimate of the spectral gap for zero-range-exclusion dynamics, Osaka Jour.Math. 141(no.4) (2004)]. This model is of non-gradient type and its spin values are unbounded so that there arise various interesting problems in the investigation of the hydrodynamic limit for the model.
The estimate obtained, though not uniform in the density of the gas as those for many known models are, seems sufficiently accurate for dealing with the problems concerning its hydrodynamic limit. In fact based on our estimate we proved in 2004 that the fluctuations around the hydrodynamic scaling in the equilibrium converge to a process that is characterized as an infinite dimensional Ornstein-Uhlenbeck prosess [cf. Equilibrium fluctuations for zero-range-exclusion processes, Jour.Stat.Phys. (2004)]. We encountered a certain difficulty for proving the tightness of a sequence of the processes of finite size and resolved it by devising a trick by using a time reversed process.
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