论文标题
布朗磁盘从边界点观看
The Brownian disk viewed from a boundary point
论文作者
论文摘要
我们根据连续的随机树的森林提供了新的布朗磁盘的结构，该森林配备了与距离在磁盘边界上均匀分布的距离远距离距离的非负标签。该结构特别表明，距离杰出点的距离沿边界发展为五维贝塞尔桥。作为我们证明的重要组成部分，我们表明，边界上的统一度量（如Bettinelli和Miermont的早期工作中所定义）是边界小管域邻域上适当归一化体积度量的极限。我们的构造还简单地证明了布朗半平面的两个定义之间的等效性。
We provide a new construction of Brownian disks in terms of forests of continuous random trees equipped with nonnegative labels corresponding to distances from a distinguished point uniformly distributed on the boundary of the disk. This construction shows in particular that distances from the distinguished point evolve along the boundary as a five-dimensional Bessel bridge. As an important ingredient of our proofs, we show that the uniform measure on the boundary, as defined in the earlier work of Bettinelli and Miermont, is the limit of the suitably normalized volume measure on a small tubular neighborhood of the boundary. Our construction also yields a simple proof of the equivalence between the two definitions of the Brownian half-plane.
