| 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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| Co-Investigator(Kenkyū-buntansha) |
福田 拓生 日本大学, 文理学部, 教授 (00009599)
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| Project Period (FY) |
2008 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 確率論 / エルゴード理論 / 疑似乱数 / エルゴート / 議事乱数 / スペクトル / 力学系 / ペロンフロベニウス作用素 / エルゴード / スペクトル半径 / 混合生 / 力学的ζ関数 / pseudo tandom number / ergodic theory / Perron-Frobenius operator / low discrepancy sequence |
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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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