| 研究課題/領域番号 |
19K03540
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| 研究種目 |
基盤研究(C)
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| 配分区分 | 基金 |
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| 応募区分 | 一般 |
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| 審査区分 |
小区分12010:基礎解析学関連
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| 研究機関 | 京都大学 |
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研究代表者 |
Croydon David 京都大学, 数理解析研究所, 准教授 (50824182)
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| 研究期間 (年度) |
2019-04-01 – 2024-03-31
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| 研究課題ステータス |
交付 (2022年度)
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| 配分額 *注記 |
4,290千円 (直接経費: 3,300千円、間接経費: 990千円)
2022年度: 650千円 (直接経費: 500千円、間接経費: 150千円)
2021年度: 1,170千円 (直接経費: 900千円、間接経費: 270千円)
2020年度: 1,300千円 (直接経費: 1,000千円、間接経費: 300千円)
2019年度: 1,170千円 (直接経費: 900千円、間接経費: 270千円)
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| キーワード | Mott hopping / Extremal process / Random walk / Localization / Random environment / random walk / percolation / subdiffusion / trapping / hear kernel estimates / uniform spanning tree / critical dimension / Mott random walk / heat kernel estimates / scaling limits / scaling limit / random walks / random graphs / fractals |
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| 研究開始時の研究の概要 |
The main aim of the project is to identify examples of random walks on random graphs to which resistance form techniques can be applied to deduce scaling limits, and derive detailed properties of the limiting processes. Specifically, the PI will consider models such as percolation clusters and uniform spanning trees, biased random walk, and the Mott variable range jump process. Proerties of the random walks and limiting diffusions considered will be heat kernel estimates, cover times and trapping phenomena.
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| 研究実績の概要 |
My main research achievement this year was the completion of a paper "Extremal regime for one-dimensional Mott variable-range hopping", jointly with Ryoki Fukushima and Stefan Junk. After the two-year period of limited research travel due to covid, I also restarted academic travels, making an extended trip to the the UK to work with Ben Hambly. I gave numerous research presentations around the UK, as well as ones in Germany and Mexico. The trip was a good chance to initiate collaborative projects.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
Generally the project has progressed as expected, and indeed, I have maybe more ongoing collaborations than I might have initially expected. Due to the limited research travel during the last two years, I have some remaining money left on the grant, which I have extended into a further year.
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| 今後の研究の推進方策 |
I have a number of ongoing collaborations relating to scaling limits, heat kernel estimates, aging, cover times and spectral properties of random walks in random environments, some of which I hope to be able to complete in the current academic year. I will use the remaining grant money to visit collaborators.
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