Numerical computations for the schramm-loewner evolution

Research output: Contribution to journalArticle

18 Scopus citations

Abstract

We review two numerical methods related to the Schramm-Loewner evolution (SLE). The first simulates SLE itself. More generally, it finds the curve in the half-plane that results from the Loewner equation for a given driving function. The second method can be thought of as the inverse problem. Given a simple curve in the half-plane it computes the driving function in the Loewner equation. This algorithm can be used to test if a given random family of curves in the half-plane is SLE by computing the driving process for the curves and testing if it is Brownian motion. More generally, this algorithm can be used to compute the driving process for random curves that may not be SLE. Most of the material presented here has appeared before. Our goal is to give a pedagogic review, illustrate some of the practical issues that arise in these computations and discuss some open problems.

Original languageEnglish (US)
Pages (from-to)839-856
Number of pages18
JournalJournal of Statistical Physics
Volume137
Issue number5
DOIs
StatePublished - Dec 1 2009

Keywords

  • Random curves
  • Schramm-Loewner evolution
  • Simulation
  • Zipper algorithm

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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