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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.

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  1. Department of Mathematics, University of Arizona, Tucson, AZ, 85721, USA

    Tom Kennedy

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  1. Tom Kennedy
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Correspondence to Tom Kennedy.

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Kennedy, T. A Fast Algorithm for Simulating the Chordal Schramm–Loewner Evolution. J Stat Phys 128, 1125–1137 (2007). https://doi.org/10.1007/s10955-007-9358-1

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  • DOI: https://doi.org/10.1007/s10955-007-9358-1

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