2022 Fiscal Year Research-status Report
Stochastic processes associated with resistance forms
| Project/Area Number |
19K03540
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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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| Keywords | Mott hopping / Extremal process / Random walk / Localization / Random environment |
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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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| Causes of Carryover |
Principally the amount remaining stems from the limited travels I undertook during covid. I plan to use it to visit collaborators, and attend a major international conference.
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