TY - JOUR

T1 - A fast algorithm for simulating the chordal Schramm-Loewner Evolution

AU - Kennedy, Tom

N1 - Funding Information:
Fig. 10 Time per point computed as a function of N. The four curves correspond to n = 8↪ 10↪ 12↪ 14. The line shown has slope 0.4 (color online) Acknowledgements The Banff International Research Station made possible many fruitful interactions. In particular, I learned much of the material in Sect. 2 from conversations with Steffen Rohde and Don Marshall. This work was supported by the National Science Foundation (DMS-0201566 and DMS-0501168).

PY - 2007/9

Y1 - 2007/9

N2 - 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.

AB - 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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U2 - 10.1007/s10955-007-9358-1

DO - 10.1007/s10955-007-9358-1

M3 - Article

AN - SCOPUS:34547759889

VL - 128

SP - 1125

EP - 1137

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 5

ER -