论文标题
径向SLE $ _ {\ infty} $的大偏差
Large deviations of radial SLE$_{\infty}$
论文作者
论文摘要
我们在带有参数$κ\ rightarrow \ rightarrow \ infty $的单位磁盘上得出了径向schramm-loewner进化（$ \ operatorname {sle} $）的大偏差原理。限制到时间间隔$ [0,1] $，良好的速率函数仅对由绝对连续的概率度量驱动的某个家族的loewner链，$ \ {ϕ_t^2（ζ）\，dζ\} _ {t \} _ {t _ {t \ in [0,1]在[0,1]} $ in [0,1]} $ in [0,1] | ϕ_t'|^2/2 \，dζ\，dt $。我们的证明依赖于大偏差原理，用于唐斯克和瓦拉达汉的长期平均水平。
We derive the large deviation principle for radial Schramm-Loewner evolution ($\operatorname{SLE}$) on the unit disk with parameter $κ\rightarrow \infty$. Restricting to the time interval $[0,1]$, the good rate function is finite only on a certain family of Loewner chains driven by absolutely continuous probability measures $\{ϕ_t^2 (ζ)\, dζ\}_{t \in [0,1]}$ on the unit circle and equals $\int_0^1 \int_{S^1} |ϕ_t'|^2/2\,dζ\,dt$. Our proof relies on the large deviation principle for the long-time average of the Brownian occupation measure by Donsker and Varadhan.
