论文标题
部分可观测时空混沌系统的无模型预测
Thick points of the planar GFF are totally disconnected for all $γ\ne 0$
论文作者
论文摘要
我们证明，具有DIRICHLET边界条件的平面高斯免费场（GFF）的$γ$厚点是A.S.完全断开所有$γ\ neq 0 $的连接。我们的证明依赖于GFF和嵌套CLE $ _4 $之间的耦合。 In particular, we show that the thick points of the GFF are the same as those of the weighted CLE$_4$ nesting field and establish the almost sure total disconnectedness of the complement of a nested CLE$_κ$, $κ\in (8/3,4]$. As a corollary we see that the set of singular points for supercritical LQG metrics is a.s. totally disconnected.
We prove that the set of $γ$-thick points of a planar Gaussian free field (GFF) with Dirichlet boundary conditions is a.s. totally disconnected for all $γ\neq 0$. Our proof relies on the coupling between a GFF and the nested CLE$_4$. In particular, we show that the thick points of the GFF are the same as those of the weighted CLE$_4$ nesting field and establish the almost sure total disconnectedness of the complement of a nested CLE$_κ$, $κ\in (8/3,4]$. As a corollary we see that the set of singular points for supercritical LQG metrics is a.s. totally disconnected.
