2013 Fiscal Year Final Research Report
Markov chains on disordered media and their scaling limits
| Project/Area Number |
22340017
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
AIKAWA Hiroaki 北海道大学, 大学院理学研究院, 教授 (20137889)
SHIGEKAWA Ichiro 京都大学, 大学院理学研究科, 教授 (00127234)
KIGAMI Jun 京都大学, 大学院情報学研究科, 教授 (90202035)
HINO Masanori 京都大学, 大学院情報学研究科, 准教授 (40303888)
UEMURA Toshihiro 関西大学, システム理工学部, 教授 (30285332)
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| Co-Investigator(Renkei-kenkyūsha) |
FUNAKI Tadahisa 東京大学, 大学院数理科学研究科, 教授 (60112174)
TAKEDA Masayoshi 東北大学, 大学院理学研究科, 教授 (30179650)
KOTANI Motoko 東北大学, 大学院理学研究科, 教授 (50230024)
YOSHIDA Nobuo 京都大学, 大学院理学研究科, 教授 (40240303)
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| Project Period (FY) |
2010-04-01 – 2013-03-31
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| Keywords | 確率論 / 数理物理 / 解析学 / 複雑系 / 統計力学 / 飛躍型確率過程 / 国際研究者交流 / イギリス：アメリカ：カナダ：ドイツ |
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| Research Abstract |
We analysed Markov chains on disordered media and their scaling limits in a unified manner by using probabilistic and analytic methods. From the viewpoint of constructing general theory, we established the following results; i) heat kernel estimates for non-symmetric Markov chains satisfying some cycle condition and analyzing their scaling limits, ii) equivalence of the sub-Gaussian heat kernel estimates and generalized Parabolic Harnack inequalities on symmetric diffusions for general metric measure spaces, iii) convergence of jump-type processes for general metric measure spaces. From the viewpoint of concrete examples, we established the following results; i) asymptotic behavior and scaling limits of biased random walks on critical percolation clusters (conditioned to survive forever) on trees, ii) convergence of scaled mixing times on Markov chains on random finite graphs.
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