定向高聚物的定域化与Perron-Frobenius理论
Localization and Perron--Frobenius theory for directed polymers
摘要：
我们考虑定向聚合物在随机电位由一个确定性的配置文件与一个强的最大值在原点采取随机符号在每个整数时间。我们研究两个主要对象的基础上，在这个随机潜在的路径。首先，我们使用随机势和平均路径定义一个抛物模型通过随机Feynman-Kac演化算子。我们发现，对于由此产生的上循环，有一个独特的正上循环本征函数作为一个向前和拉回吸引子。其次，我们利用势定义了任意有界时间区间上路径的Gibbs规范，并研究了无穷体积Gibbs测度的热力学极限和存在唯一性。这两个主要的结果都声称，相互作用的局部结构导致一个独特的宏观对象几乎每一个实现的随机潜力。
英文摘要：
We consider directed polymers in a random potential given by a deterministic profile with a strong maximum at the origin taken with random sign at each integer time. We study two main objects based on paths in this random potential. First, we use the random potential and averaging over paths to define a parabolic model via a random Feynman--Kac evolution operator. We show that for the resulting cocycle, there is a unique positive cocycle eigenfunction serving as a forward and pullback attractor. Secondly, we use the potential to define a Gibbs specification on paths for any bounded time interval in the usual way and study the thermodynamic limit and existence and uniqueness of an infinite volume Gibbs measure. Both main results claim that the local structure of interaction leads to a unique macroscopic object for almost every realization of the random potential.
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