| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
I investigated \phi-Gaussian measures, which is obtained by generalizing the Gaussian measure via a positive continuous non-decreasing function \phi on the positive half line. If \phi is the identity function then the \phi-Gaussian measure recovers the Gaussian measure,and in the case that \phi is the power function with exponent q which lies in (0,1) or (1,2), the \phi-Gaussian measure is a power distribution, so-called the q-Gaussian measure.
In the joint work with Shin-ichi Ohta, we provided a useful condition to we analyze a metric measure space based on the theory of the q- Gaussian measure. By using this condition, we obtained analytic/geometric results such as a set of functional inequalities (e.g. a transport inequality), the concentration of measure phenomenon (which describes a relation between volume and distance) and the gradient flow of the \phi-divergence on the Wasserstein space.
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