A fast algorithm for simulating the chordal Schramm-Loewner Evolution

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Abstract

The Schramm-Loewner evolution (SLE) can be simulated by dividing the time interval into N subintervals and approximating the random conformal map of the SLE by the composition of N random, but relatively simple, conformal maps. In the usual implementation the time required to compute a single point on the SLE curve is O(N). We give an algorithm for which the time to compute a single point is O(N p ) with p<1. Simulations with κ=8/3 and κ=6 both give a value of p of approximately 0.4.

Original languageEnglish (US)
Pages (from-to)1125-1137
Number of pages13
JournalJournal of Statistical Physics
Volume128
Issue number5
DOIs
Publication statusPublished - Sep 2007

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ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

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