A Guide to Stochastic Löwner Evolution and Its Applications
A Guide to Stochastic Löwner Evolution and Its Applications
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DOI：
10.1023/b:joss.0000028058.87266.be
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发表时间：
2003-12
影响因子：
1.6
通讯作者：
W. Kager;B. Nienhuis
中科院分区：
文献类型：
--
作者：
W. Kager;B. Nienhuis
这篇文章的目的是作为一个指南，在临界模型的标度极限研究的最新进展。这些新的发展是通过Oded Schramm对随机Löwner演化（SLE）的定义而成为可能的。本文首先讨论Löwner方法，解释如何使用该方法来描述随机曲线族。然后我们定义了SLE并讨论了它的一些性质。我们还解释了如何可以SLE和离散模型的缩放限制，它描述，或被认为是描述之间的连接。最后，我们讨论了从SLE计算中获得的结果。一些明确的证明，作为这种计算的典型例子。要理解SLE，需要有足够的共形映射理论和随机微积分的知识。附录中涵盖了该材料。
This article is meant to serve as a guide to recent developments in the study of the scaling limit of critical models. These new developments were made possible through the definition of the Stochastic Löwner Evolution (SLE) by Oded Schramm. This article opens with a discussion of Löwner's method, explaining how this method can be used to describe families of random curves. Then we define SLE and discuss some of its properties. We also explain how the connection can be made between SLE and the discrete models whose scaling limits it describes, or is believed to describe. Finally, we have included a discussion of results that were obtained from SLE computations. Some explicit proofs are presented as typical examples of such computations. To understand SLE sufficient knowledge of conformal mapping theory and stochastic calculus is required. This material is covered in the appendices.