2012 Fiscal Year Final Research Report
Research on the spectrum of Perron-Frobenius operator and pseudo random number associated with higher dimensional dynamical system
| Project/Area Number |
20540139
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Nihon University |
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Principal Investigator |
MORI Makoto 日本大学, 文理学部, 教授 (60092532)
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| Project Period (FY) |
2008 – 2012
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| Keywords | 確率論 |
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| Research Abstract |
In 1-dimensional cases, the essential spectrum radius of thePerron-Frobenius operator takes its minimum value, and it is easy to calculate it.However, in higher dimensional cases, it is important to consider the cases when its unessential spectrum radius takes its minimum value, and it is not easy to construct dynamical systems for which the essential spectrum radius attains its minimum value. We construct such a dynamical system which has no eigenvalue except 1 by using algebraic method. From this dynamical system, we construct low discrepancy sequences in any dimension. This makes a new progression to computer science such as simulation and numerical integral in stochastic integrals. On the other hand, this research suggests the difficulty of constructing dynamical system which has minimal essential spectrum radius, and the difficulty of constructing “good” random numbers in higher dimensional cases.
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Research Products
(21 results)
