2013 Fiscal Year Final Research Report
Studies on dynamics of one-dimensional exclusion processes
| Project/Area Number |
22740054
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Chiba University |
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Principal Investigator |
SASAMOTO Tomohiro 千葉大学, 理学(系)研究科(研究院), 准教授 (70332640)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 無限粒子系 / 確率過程 / 統計力学 / ランダム行列 |
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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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