Phase Transitions for the Growth Rate of Linear Stochastic Evolutions
Phase Transitions for the Growth Rate of Linear Stochastic Evolutions
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DOI：
10.1007/s10955-008-9646-4
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发表时间：
2008-05
影响因子：
1.6
通讯作者：
N. Yoshida
中科院分区：
文献类型：
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作者：
N. Yoshida
本文考虑了一维格点上的离散时间随机增长模型。生长模型描述了各种有趣的例子，如定向位点/键渗流，定向聚合物在随机环境中，时间离散化的二元接触路径过程和选民模型。我们在这个框架下研究了“粒子总数”增长率的相变。主要结果大致如下：如果fd ≥3且系统“不太随机”，则在正概率下，粒子总数的增长率与其期望值在同一数量级。另一方面，如果d= 1，2，或者系统“足够随机”，那么增长率比它的预期要慢。我们还讨论了对偶过程的上述相变及其与具有适当归一化的模型的不变测度结构的联系。
We consider a discrete-time stochastic growth model ond-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: Ifd≥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. We also discuss the above phase transition for the dual processes and its connection to the structure of invariant measures for the model with proper normalization.