规范SLE可逆的Weil--Petersson响应扩散

中文摘要 AI 辅助

针对旋转标记的SLE焊接律的粗糙响应演算给出了一个封闭的Weil--Petersson能量，但本身并未给出粗糙焊接上的过程。对于$0<\kappa\leq4$，我们证明该形式在圆周同胚的自然拓扑中是拟正则的，因此生成一个关于SLE焊接概率可逆的规范扩散。证明通过逆弧质量构造了一个紧致形式巢。我们将生成元识别为$-D^*D$，并证明其Fourier展开在响应圆柱核心上的绝对$L^2$收敛，以及Fukushima分解。一个共同的Fourier噪声和防止边界塌陷的平面估计给出了由归一化Jordan焊接三元组实现的第二个拟正则实现。该扩散是不可约的，并在$L^2$中强收敛到平衡态。对于$0<\kappa<4$，共形可移除焊接轨迹的补集具有零容量。

英文摘要

The rough response calculus for the rotationally marked SLE welding law gives a closed Weil--Petersson energy but does not by itself give a process on rough weldings. For $0<κ\leq4$, we prove that this form is quasi-regular in the natural topology of circle homeomorphisms and therefore generates a canonical diffusion reversible with respect to the SLE welding probability. The proof constructs a compact form nest from inverse arc masses. We identify the generator as $-D^*D$ and prove absolute $L^2$ convergence of its Fourier expansion on the response cylinder core, together with the Fukushima decomposition. A common Fourier noise and planar estimates preventing boundary collapse yield a second quasi-regular realization by normalized Jordan welding triples. The diffusion is irreducible and converges strongly in $L^2$ to equilibrium. For $0<κ<4$, the complement of the conformally removable welding locus has zero capacity.

发表机构

• School of Mathematics (Zhuhai), Sun Yat-Sen University（中山大学数学学院（珠海））

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