论文标题
CLE_4循环的极距离和共形半径
Extremal distance and conformal radius of a CLE_4 loop
论文作者
论文摘要
考虑单位磁盘中的cle $ _4 $，让$ \ ell $为围绕原点的cle $ _4 $的环。 Schramm，Sheffield和Wilson确定了从$ \ ell $包围的域的起源中看到的保形半径的定律。我们通过确定$ \ ell $和单位磁盘边界之间的极端距离的法律来补充他们的结果。更令人惊讶的是，我们还计算了这些保形半径和极端距离的联合定律。该法律涉及一维布朗尼运动的第一和最后一次打击时间。类似的技术还使我们能够确定关键的布朗循环群集群中某些极端距离的联合定律。
Consider CLE$_4$ in the unit disk and let $\ell$ be the loop of the CLE$_4$ surrounding the origin. Schramm, Sheffield and Wilson determined the law of the conformal radius seen from the origin of the domain surrounded by $\ell$. We complement their result by determining the law of the extremal distance between $\ell$ and the boundary of the unit disk. More surprisingly, we also compute the joint law of these conformal radius and extremal distance. This law involves first and last hitting times of a one-dimensional Brownian motion. Similar techniques also allow us to determine joint laws of some extremal distances in a critical Brownian loop-soup cluster.
