论文标题
关于随机纠缠问题
On a random entanglement problem
论文作者
论文摘要
我们研究了一个模型，用于在有界区域中反映布朗尼运动的二维反映布朗运动的模型，该模型被带有三个或更多小窗户的壁分为两半。我们将布朗运动映射到该地区基本类的马尔可夫链中。我们将路径的纠缠与该群体中适当元素的长度的长度量化。我们的主要结果是大量定律和此数量的中心限制定理。出现在极限定理中的常数以二次方程的耦合系统表示。
We study a model for the entanglement of a two-dimensional reflecting Brownian motion in a bounded region divided into two halves by a wall with three or more small windows. We map the Brownian motion into a Markov Chain on the fundamental groupoid of the region. We quantify entanglement of the path with the length of the appropriate element in this groupoid. Our main results are a law of large numbers and a central limit theorem for this quantity. The constants appearing in the limit theorems are expressed in terms of a coupled system of quadratic equations.
