Computing the loewner driving process of random curves in the half plane

Research output: Contribution to journalArticle

13 Scopus citations

Abstract

We simulate several models of random curves in the half plane and numerically compute the stochastic driving processes that produce the curves through the Loewner equation. Our models include models whose scaling limit is the Schramm-Loewner evolution (SLE) and models for which it is not. We study several tests of whether the driving process is Brownian motion, as it is for SLE. We find that testing only the normality of the process at a fixed time is not effective at determining if the random curves are an SLE. Tests that involve the independence of the increments of Brownian motion are much more effective. We also study the zipper algorithm for numerically computing the driving function of a simple curve. We give an implementation of this algorithm which runs in a time O(N 1.35) rather than the usual O(N 2), where N is the number of points on the curve.

Original languageEnglish (US)
Pages (from-to)803-819
Number of pages17
JournalJournal of Statistical Physics
Volume131
Issue number5
DOIs
StatePublished - Jun 1 2008

Keywords

  • Loewner equation
  • Random curves
  • SLE
  • Zipper algorithm

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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