Probability Theory and Related Fields ( IF 2 ) Pub Date : 2021-04-28 , DOI: 10.1007/s00440-021-01033-9 Vivian Olsiewski Healey , Gregory F. Lawler
We use the interpretation of the Schramm–Loewner evolution as a limit of path measures tilted by a loop term in order to motivate the definition of n-radial SLE going to a particular point. In order to justify the definition we prove that the measure obtained by an appropriately normalized loop term on n-tuples of paths has a limit. The limit measure can be described as n paths moving by the Loewner equation with a driving term of Dyson Brownian motion. While the limit process has been considered before, this paper shows why it naturally arises as a limit of configurational measures obtained from loop measures.
中文翻译:
N面径向Schramm–Loewner演化
我们使用Schramm-Loewner演化的解释作为由环项倾斜的路径量度的极限,以激发n径向SLE定义的特定点。为了证明该定义的正确性,我们证明了通过对路径的n个元组进行适当归一化的循环项获得的度量是有限制的。极限测度可以描述为通过Loewner方程以Dyson Brownian运动的驱动项运动的n条路径。虽然之前已经考虑过极限过程,但本文显示了为什么它自然地成为从环路测度获得的配置测度的极限。