A Guide to Stochastic Loewner Evolution and its Applications

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dc.creatorKager, Wouter
dc.creatorNienhuis, Bernard
dc.date2003-12-22
dc.date2004-07-27
dc.date.accessioned2026-07-07T04:30:50Z
dc.date.available2026-07-07T04:30:50Z
dc.descriptionThis 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.
dc.description80 pages, 22 figures, LaTeX; this version has 5 minor corrections to the text and improved hyperref support
dc.identifierhttps://arxiv.org/abs/math-ph/0312056
dc.identifierhttp://arxiv.org/abs/math-ph/0312056
dc.identifierJ. Stat. Phys. 115:1149-1229 (2004)
dc.identifierdoi:10.1023/B:JOSS.0000028058.87266.be
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57606
dc.subjectMathematical Physics
dc.subjectStatistical Mechanics
dc.subjectHigh Energy Physics - Theory
dc.subjectProbability
dc.titleA Guide to Stochastic Loewner Evolution and its Applications
dc.typetext

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