论文标题
定位聚合物的联合定位
Joint localization of directed polymers
论文作者
论文摘要
我们考虑$（1+1）$ - 尺寸为定向的聚合物，并提供足够的条件来保证联合定位。联合定位意味着，对于典型的环境实现，对于聚合物，从不同的起点开始，所有相关的端点分布都定位在不随着聚合物长度而生长的常见随机区域。特别是，当聚合物模型的参考随机步行是简单的对称晶格步行或高斯随机步行时，我们证明关节定位会成立。我们还证明，非常强大的障碍特性适用于大量的连续聚合物模型，这意味着通常的单一聚合物定位。
We consider $(1+1)$-dimensional directed polymers in a random potential and provide sufficient conditions guaranteeing joint localization. Joint localization means that for typical realizations of the environment, and for polymers started at different starting points, all the associated endpoint distributions localize in a common random region that does not grow with the length of the polymer. In particular, we prove that joint localization holds when the reference random walk of the polymer model is either a simple symmetric lattice walk or a Gaussian random walk. We also prove that the very strong disorder property holds for a large class of space-continuous polymer models, implying the usual single polymer localization.
