2017 Fiscal Year Final Research Report
Analysis of branching process with interacting particle systems
| Project/Area Number |
26800051
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Nagoya University (2015-2017)
University of Tsukuba (2014) |
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Principal Investigator |
Nakashima Makoto 名古屋大学, 多元数理科学研究科, 准教授 (60635902)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Keywords | 統計力学 / ディレクティドポリマー / 相転移 / 臨界点 / ピニング模型 / 分枝ランダムウォーク |
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| Outline of Final Research Achievements |
Asymptotics of logarithms of the total number of branching random walks in random environment are controlled by the free energy of directed polymers in random environment.
We gave estimates of free energies for directed polymers in random environment in 1 and 2 dimensions.
Also, we study the random walk pinning model to analyze the critical points of directed polymers in random environment in higher dimension. We found that two critical points coincide with each other and we proved the central limit theorem and invariance principle in the subcritical phase for dimension d\geq 3.
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| Free Research Field |
確率論
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