论文标题
$ 1+1 $ continuum指导的随机聚合物的本地化长度
Localization length of the $1+1$ continuum directed random polymer
论文作者
论文摘要
在本文中，我们研究了$ 1+1 $连续的指向聚合物的定位长度，该长度定义为与淬灭聚合物度量独立采样的两个路径的端点之间的距离。我们表明，定位长度在热力学极限的分布中收敛，并得出了极限分布的显式密度公式。结果，我们证明了密度的$ \ tfrac32 $ powerappower法律衰减，证实了hwa-fisher \ cite {fisher}的物理预测。我们的证明使用了das-zhu \ cite {daszhu}的最新结果。
In this paper, we study the localization length of the $1+1$ continuum directed polymer, defined as the distance between the endpoints of two paths sampled independently from the quenched polymer measure. We show that the localization length converges in distribution in the thermodynamic limit, and derive an explicit density formula of the limiting distribution. As a consequence, we prove the $\tfrac32$-power law decay of the density, confirming the physics prediction of Hwa-Fisher \cite{fisher}. Our proof uses the recent result of Das-Zhu \cite{daszhu}.
