### Abstract

We review two numerical methods related to the Schramm-Loewner evolution (SLE). The first simulates SLE itself. More generally, it finds the curve in the half-plane that results from the Loewner equation for a given driving function. The second method can be thought of as the inverse problem. Given a simple curve in the half-plane it computes the driving function in the Loewner equation. This algorithm can be used to test if a given random family of curves in the half-plane is SLE by computing the driving process for the curves and testing if it is Brownian motion. More generally, this algorithm can be used to compute the driving process for random curves that may not be SLE. Most of the material presented here has appeared before. Our goal is to give a pedagogic review, illustrate some of the practical issues that arise in these computations and discuss some open problems.

Original language | English (US) |
---|---|

Pages (from-to) | 839-856 |

Number of pages | 18 |

Journal | Journal of Statistical Physics |

Volume | 137 |

Issue number | 5 |

DOIs | |

State | Published - Dec 2009 |

### Fingerprint

### Keywords

- Random curves
- Schramm-Loewner evolution
- Simulation
- Zipper algorithm

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

**Numerical computations for the schramm-loewner evolution.** / Kennedy, Thomas G.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 137, no. 5, pp. 839-856. https://doi.org/10.1007/s10955-009-9866-2

}

TY - JOUR

T1 - Numerical computations for the schramm-loewner evolution

AU - Kennedy, Thomas G

PY - 2009/12

Y1 - 2009/12

N2 - We review two numerical methods related to the Schramm-Loewner evolution (SLE). The first simulates SLE itself. More generally, it finds the curve in the half-plane that results from the Loewner equation for a given driving function. The second method can be thought of as the inverse problem. Given a simple curve in the half-plane it computes the driving function in the Loewner equation. This algorithm can be used to test if a given random family of curves in the half-plane is SLE by computing the driving process for the curves and testing if it is Brownian motion. More generally, this algorithm can be used to compute the driving process for random curves that may not be SLE. Most of the material presented here has appeared before. Our goal is to give a pedagogic review, illustrate some of the practical issues that arise in these computations and discuss some open problems.

AB - We review two numerical methods related to the Schramm-Loewner evolution (SLE). The first simulates SLE itself. More generally, it finds the curve in the half-plane that results from the Loewner equation for a given driving function. The second method can be thought of as the inverse problem. Given a simple curve in the half-plane it computes the driving function in the Loewner equation. This algorithm can be used to test if a given random family of curves in the half-plane is SLE by computing the driving process for the curves and testing if it is Brownian motion. More generally, this algorithm can be used to compute the driving process for random curves that may not be SLE. Most of the material presented here has appeared before. Our goal is to give a pedagogic review, illustrate some of the practical issues that arise in these computations and discuss some open problems.

KW - Random curves

KW - Schramm-Loewner evolution

KW - Simulation

KW - Zipper algorithm

UR - http://www.scopus.com/inward/record.url?scp=74649083449&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=74649083449&partnerID=8YFLogxK

U2 - 10.1007/s10955-009-9866-2

DO - 10.1007/s10955-009-9866-2

M3 - Article

VL - 137

SP - 839

EP - 856

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 5

ER -