Large deviations of multichordal $\operatorname{SLE}_{0+}$, real rational functions, and zeta-regularized determinants of Laplacians
Large deviations of multichordal $\operatorname{SLE}_{0+}$, real rational functions, and zeta-regularized determinants of Laplacians
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多弦 $operatorname{SLE}_{0 }$、实有理函数和拉普拉斯 zeta 正则化行列式的大偏差
DOI：
10.4171/jems/1274
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发表时间：
2020
影响因子：
2.6
通讯作者：
Yilin Wang
中科院分区：
文献类型：
--
作者：
Eveliina Peltola;Yilin Wang
本文证明了多重弦SLE${0+}$曲线关于Hausdorff度量的一个强大偏差原理。在单弦情况下，这个结果加强了第二作者早先的部分结果。我们还介绍了一个Loewner潜在的，在光滑的情况下，有一个简单的表达式在zeta正则化的拉普拉斯行列式。这个潜在的不同LDP率函数的添加剂常数仅取决于边界数据，满足PDE产生的经典极限的Belavin-Polyakov-Zamolodchikov方程的水平2共形场论与中心电荷$c \到-\infty$。
此外，我们表明，每个多弦最小化潜在的上半平面为一个给定的边界数据是一个有理函数的真实的轨迹是唯一的，从而符合$\kappa \到0+$限制的多个SLE$_\kappa$。作为一个副产品，我们提供了一个解析证明夏皮罗猜想在真实的枚举几何，首先证明了Eremenko和Gabrielov：如果所有的临界点的有理函数是真实的，那么该功能是真实的后组成的莫比乌斯映射。
We prove a strong large deviation principle (LDP) for multiple chordal SLE$_{0+}$ curves with respect to the Hausdorff metric. In the single chordal case, this result strengthens an earlier partial result by the second author. We also introduce a Loewner potential, which in the smooth case has a simple expression in terms of zeta-regularized determinants of Laplacians. This potential differs from the LDP rate function by an additive constant depending only on the boundary data, that satisfies PDEs arising as a classical limit of the Belavin-Polyakov-Zamolodchikov equations of level two in conformal field theory with central charge $c \to -\infty$.
Furthermore, we show that every multichord minimizing the potential in the upper half-plane for a given boundary data is the real locus of a rational function and is unique, thus coinciding with the $\kappa \to 0+$ limit of the multiple SLE$_\kappa$. As a by-product, we provide an analytic proof of the Shapiro conjecture in real enumerative geometry, first proved by Eremenko and Gabrielov: if all critical points of a rational function are real, then the function is real up to post-composition by a Mobius map.
循环的Loewner能量和驱动函数的正则性
影响因子：
1
作者：
Rohde, Steffen;Wang, Yilin
通讯作者：
Wang, Yilin