2003/12/31 by Wouter Kager, Bernard Nienhuis · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #hep-th #math-ph #math.MP #math.PR
paper · pdf · doi:10.1023/b:joss.0000028058.87266.be
published as J. Stat. Phys. 115:1149-1229 (2004) · 80 pages, 22 figures, LaTeX; this version has 5 minor corrections to the text and improved hyperref support
openalex publication_date 2004/05/19 · arxiv created 2004/07/27 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 Loewner Evolution (SLE) by Oded Schramm. This article opens with a discussion of Loewner'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.