A Fast Algorithm for Simulating the Chordal Schramm-Loewner Evolution

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 kappa=8/3 and kappa=6 both give a value of p of approximately 0.4.

17 pages, 10 figures. Version 2 revisions: added a paragraph to introduction, added 5 references and corrected a few typos

References in corpus (3)

• Conformal invariance in two-dimensional turbulence
• Inverse turbulent cascades and conformally invariant curves
• Are Domain Walls in Spin Glasses Described by Stochastic Loewner Evolutions?

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