### 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 language | English (US) |
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Pages (from-to) | 1125-1137 |

Number of pages | 13 |

Journal | Journal of Statistical Physics |

Volume | 128 |

Issue number | 5 |

DOIs | |

State | Published - Sep 2007 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

**A fast algorithm for simulating the chordal Schramm-Loewner Evolution.** / Kennedy, Thomas G.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 128, no. 5, pp. 1125-1137. https://doi.org/10.1007/s10955-007-9358-1

}

TY - JOUR

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

AU - Kennedy, Thomas G

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.

UR - http://www.scopus.com/inward/record.url?scp=34547759889&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34547759889&partnerID=8YFLogxK

U2 - 10.1007/s10955-007-9358-1

DO - 10.1007/s10955-007-9358-1

M3 - Article

VL - 128

SP - 1125

EP - 1137

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 5

ER -