2016 Fiscal Year Final Research Report
Study on random fields with long range correlations related to phase separating interfaces
| Project/Area Number |
26400147
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Keio University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Keywords | 界面モデル / 相転移 / Gauss場 / Gibbs測度 / 自由エネルギー |
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| Outline of Final Research Achievements |
In this research, we studied several random fields with long range correlations for mathematical analysis of phase separating interfaces and membranes. In particular, we considered the Δφ interface model and obtained the following results:
(1) We give an estimate on the probability that the field stays positive in low dimensions and its behaviors differ greatly from those of the higher dimensional case or other random interface models.(2) We show that in the case of two or more dimensions, once we impose weak pinning potentials the field is always localized in the sense that the corresponding free energy is always positive.
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| Free Research Field |
確率論
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