2023 Fiscal Year Final Research Report
Construction of cross-sectional theory on those conformally invariant random fields which extend SLE
| Project/Area Number |
22K20341
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Multi-year Fund |
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| Review Section |
0201:Algebra, geometry, analysis, applied mathematics,and related fields
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| Research Institution | Kyushu University |
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Principal Investigator |
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| Project Period (FY) |
2022-08-31 – 2024-03-31
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| Keywords | 小松・レヴナー微分方程式 / 縢りブラウン運動 / レヴナー微分方程式 / シュラム・レヴナー発展 |
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| Outline of Final Research Achievements |
Aiming at deep analysis of Schramm-Loewner evolution (SLE), we implemented research from perspectives of probability theory and complex analysis. Our main interest was how to extend the mathematical definition of SLE from simply connected planar domains to more general domains. In that direction, we published a book with two co-authors and made the foundation of our study clearer and solider. In another direction, we made effort to increase opportunities of research communication and, as a result, recognized new applications and problems on the Loewner differential equations.
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| Free Research Field |
確率論，複素解析
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| Academic Significance and Societal Importance of the Research Achievements |
SLEは統計物理における2次元の古典スピン系の臨界現象を記述する上で重要とされる確率過程である．複素解析におけるレヴナー微分方程式をランダムなブラウン運動で駆動して得られることが特徴であり，数理物理への寄与という意味でも，確率論・函数論の非自明な関係の開拓という意味でも興味深い．特に本研究は，レヴナー微分方程式の適用範囲を拡げたり，古典的に知られた設定を新たな視点で捉え直したりといった，基礎理論への寄与の点で意義を持つ．
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