| Project/Area Number |
16K21039
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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
Foundations of mathematics/Applied mathematics
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| Research Institution | Yokohama National University |
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Principal Investigator |
TAKEI Masato 横浜国立大学, 大学院工学研究院, 准教授 (60460789)
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| Research Collaborator |
AKAHORI Jiro
COLLEVECCHIO Andrea
ISHIKAWA Tomohiro
KOUDUMA Ryouta
KUBOTA Naoki
NASU Erina
OSAKA Shoto
UEMATSU Yuma
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
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: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | パーコレーション / ランダムウォーク / セルオートマトン / 量子ウォーク / 極限定理 / 相転移 |
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| Outline of Final Research Achievements |
Percolation process was originally introduced as a model of penetration of fluids into porous media. Nowadays it is one of the most fundamental stochastic models concerning random geometry. From the viewpoint of percolation theory, we studied limit theorems for several stochastic models with spatio-temporal interactions. We obtained several kinds of limit theorems for Ising percolation, (stochastic) cellular automata, random walks with memory effect, and so on. Among others we briefly describe our result on reinforced random walks: Consider a graph, and assign weight one to each edge. The walker jumps to one of the neighboring vertices with probability proportional to weight of the edge connecting them. After crossing an edge, its weight is increased by one. If the underlying graph is a b-regular tree with b>1, then the walker returns to the starting point only finitely many times with probability one. We obtain a limit theorem describing the trajectory of the walker for b>3.
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| Academic Significance and Societal Importance of the Research Achievements |
空間構造をもった確率モデルは，物理・化学・生物現象の研究においてのみならず，人々の意見が合意に達するか否かといった社会現象の研究等においても重要な役割を果たしており，多様な現象のモデル構築と解析を可能にすることが求められている．本研究では，浸透現象の数学的解析における様々な着想を基盤とし，記憶があり学習しながら歩むランダムウォーク等に関する成果を得て，この方面の研究に一定の寄与をした．
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