The covariant measure of SLE on the boundary
The covariant measure of SLE on the boundary
复制标题
SLE 边界上的协变测度
DOI：
10.1007/s00440-009-0252-4
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发表时间：
2008
影响因子：
2
通讯作者：
S. Sheffield
中科院分区：
文献类型：
--
作者：
Tom Alberts;S. Sheffield
我们构造了一个自然测度μ，它支撑在弦SLE（κ）曲线γ与$${\mathbb{R}}$$的交点上，在范围4 < κ < 8。该度量是所讨论的SLE路径的函数。假设边界测度以“d维”的方式变换（其中d是$${\gamma \cap \mathbb{R}}$$的Hausdorff维数），我们证明了我们构造的测度是满足Domain Markov性质的SLE路径的唯一测度值函数（直到乘法常数）.
We construct a natural measure μ supported on the intersection of a chordal SLE(κ) curve γ with $${\mathbb{R}}$$ , in the range 4 < κ < 8. The measure is a function of the SLE path in question. Assuming that boundary measures transform in a “d-dimensional” way (where d is the Hausdorff dimension of $${\gamma \cap \mathbb{R}}$$), we show that the measure we construct is (up to multiplicative constant) the unique measure-valued function of the SLE path that satisfies the Domain Markov property.