| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Research Abstract |
We have studied fluctuation properties of the Kardar-Parisi-Zhang (KPZ) equation and its discrete analogues, which are known to describe growing interfaces. By applying the replica techniques, we obtained explicit formulas for the one point height distribution and space-time two point correlation functions in the stationary state. These quantities had been studied by using various approximate methods from physics. Our explicit formulas do not involve any approximation and should be useful for further studies. In addition we have shown that one can study fluctuation properties of these processes in a systematic way by combining duality for interacting particle systems and some techniques from integrable systems like Bethe ansatz. We have also studied multi-point distribution for the KPZ equation, multi-component exclusion processes and KPZ equations.
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