| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Outline of Final Research Achievements |
We study a connected nonparabolic, or transient network compactified with the Kuramochi boundary, and show that the random walk converges almost surely to a random variable valued in the harmonic boundary, and a function of finite Dirichlet energy converges along the random walk to a random variable almost surely and in L2. We also give integral representations of solutions of Poisson equations on the Kuramochi compactification. We also study finite connected graphｓ which admit quasi monomorphismｓ to hyperbolic spaces and give geometric bounds for the Cheeger constants in terms of the volume, an upper bound of the degree, and the quasi monomorphism. Moreover we develop a potential theory of nonlinear networks in the frame work of modular sequence spaces.
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