Probabilistic derivation of asymptotic estimates of heat kernels and study of convex inequalities
| Project/Area Number |
24740080
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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
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| Research Institution | Tohoku University |
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Principal Investigator |
HARIYA Yuu 東北大学, 理学(系)研究科(研究院), 准教授 (20404030)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 確率解析 |
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| Outline of Final Research Achievements |
1. The Brascamp-Lieb inequality has importance in statistical mechanics, such as in the analysis of interface models. We give a simple proof of the inequality based on stochastic analysis; as an application of our method, also derived are error estimates of the inequality and its extensions to nonconvex potentials.
2. We recover the principle terms in asymptotic estimates for tail probabilities of first hitting times of Bessel process in a relatively simple manner based on the weak convergence of probability measures; sharp asymptotics of remainder terms are also derived.
3. We clarify sufficient conditions for expectations of the Feynman-Kac type with singular potentials to diverge in the following three cases: Brownian motion, symmetric stable process, and Brownian motion in the half-space with singular potentials on the boundary.
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Report
(4 results)
Research Products
(7 results)
