Large deviations of Schramm-Loewner evolutions: A survey
Large deviations of Schramm-Loewner evolutions: A survey
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DOI：
10.1214/22-ps9
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发表时间：
2021-02
影响因子：
1.6
通讯作者：
Yilin Wang
中科院分区：
文献类型：
--
作者：
Yilin Wang
这些笔记调查了 Schramm-Loewner 演化 (SLE) 大偏差的第一个结果，重点是速率函数和复杂分析应用之间的相互关系。更准确地说，我们描述了当 $\kappa$ 参数在弦和多弦情况下趋于零以及在径向情况下趋于无穷大时 SLE$_\kappa$ 的大偏差。速率函数，即 Loewner 和 Loewner-Kufarev 能量，与 Weil-Petersson 类拟圆和实有理函数密切相关。
These notes survey the first results on large deviations of Schramm-Loewner evolutions (SLE) with emphasis on interrelations between rate functions and applications to complex analysis. More precisely, we describe the large deviations of SLE$_\kappa$ when the $\kappa$ parameter goes to zero in the chordal and multichordal case and to infinity in the radial case. The rate functions, namely Loewner and Loewner-Kufarev energies, are closely related to the Weil-Petersson class of quasicircles and real rational functions.