2012 Fiscal Year Final Research Report
stochastic growth models in random environments and their phase transition
| Project/Area Number |
21540125
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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 | Kyoto University |
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Principal Investigator |
YOSHIDA Nobuo 京都大学, 大学院・理学研究科, 准教授 (40240303)
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| Project Period (FY) |
2009 – 2012
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| Keywords | ランダム環境 / 相転移 |
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| Research Abstract |
We consider a discrete-time stochastic growth model on d-dimensional lattice.The growth model describes various interesting examples such as oriented site/bond percolation, directed polymers in random environment, time discretizations of binary contact path process and the voter model. We study the phase transition for the growth rate of the ``total number of particles" in this framework.
The main results are roughly as follows: If d ≧ 3 and the system is ``not too random", then, with positive probability, the growth rate of the total number of particles is of the same order as its expectation. If on the other hand, d=1,2, or the system is ``random enough", then the growth rate is slower than its expectation.
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