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
SN - 0022-4715
VL - 128
SP - 1125
EP - 1137
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 5
ER -