论文标题
多料中SLE $ _ {0+} $的大偏差，实际有理功能和zeta regarlized laplacians的决定因素
Large deviations of multichordal SLE$_{0+}$, real rational functions, and zeta-regularized determinants of Laplacians
论文作者
论文摘要
对于Hausdorff指标，我们证明了多个和弦SLE $ _ {0+} $曲线的强大偏差原理（LDP）。在单调的情况下，该结果增强了第二作者的早期部分结果。我们还引入了Loewner电位，在平滑情况下，它在Zeta调查的laplacians的决定因素方面具有简单的表达。该电位与LDP速率函数的不同之处在于仅取决于边界数据的添加剂常数，该边界数据满足了PDE作为Belavin-Polyakov-Zamolodchikov的半经典限制，该级别的第二级和中心电荷$ C \ to-t to-t to-f to-\ infty $。 此外，我们表明，对于给定边界数据，每个多键都可以最大程度地降低上半平面中的电势，这是一个理性函数的真实轨迹，并且是唯一的，因此与$κ\至0+$限制的$κ$_κ$相吻合。作为一种副产品，我们提供了shapiro猜想中的分析证明，这是由Eremenko和Gabrielov首先证明的：如果合理函数的所有关键点都是真实的，那么该函数实际上是由Möbius转换来实现的。
We prove a strong large deviation principle (LDP) for multiple chordal SLE$_{0+}$ curves with respect to the Hausdorff metric. In the single-chord 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 semiclassical 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 given boundary data is the real locus of a rational function and is unique, thus coinciding with the $κ\to 0+$ limit of the multiple SLE$_κ$. 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 Möbius transformation.
