| Project/Area Number |
19K03540
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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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| Review Section |
Basic Section 12010:Basic analysis-related
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| Research Institution | Kyoto University |
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Principal Investigator |
Croydon David 京都大学, 数理解析研究所, 准教授 (50824182)
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| Project Period (FY) |
2019-04-01 – 2024-03-31
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| Project Status |
Granted (Fiscal Year 2022)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2022: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2021: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2020: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2019: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 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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| Outline of Research at the Start |
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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| Outline of Annual Research Achievements |
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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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
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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| Strategy for Future Research Activity |
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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