### Abstract

We simulate several models of random curves in the half plane and numerically compute the stochastic driving processes that produce the curves through the Loewner equation. Our models include models whose scaling limit is the Schramm-Loewner evolution (SLE) and models for which it is not. We study several tests of whether the driving process is Brownian motion, as it is for SLE. We find that testing only the normality of the process at a fixed time is not effective at determining if the random curves are an SLE. Tests that involve the independence of the increments of Brownian motion are much more effective. We also study the zipper algorithm for numerically computing the driving function of a simple curve. We give an implementation of this algorithm which runs in a time O(N ^{1.35}) rather than the usual O(N ^{2}), where N is the number of points on the curve.

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

Pages (from-to) | 803-819 |

Number of pages | 17 |

Journal | Journal of Statistical Physics |

Volume | 131 |

Issue number | 5 |

DOIs | |

State | Published - Jun 2008 |

### Fingerprint

### Keywords

- Loewner equation
- Random curves
- SLE
- Zipper algorithm

### ASJC Scopus subject areas

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

### Cite this

**Computing the loewner driving process of random curves in the half plane.** / Kennedy, Thomas G.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 131, no. 5, pp. 803-819. https://doi.org/10.1007/s10955-008-9535-x

}

TY - JOUR

T1 - Computing the loewner driving process of random curves in the half plane

AU - Kennedy, Thomas G

PY - 2008/6

Y1 - 2008/6

N2 - We simulate several models of random curves in the half plane and numerically compute the stochastic driving processes that produce the curves through the Loewner equation. Our models include models whose scaling limit is the Schramm-Loewner evolution (SLE) and models for which it is not. We study several tests of whether the driving process is Brownian motion, as it is for SLE. We find that testing only the normality of the process at a fixed time is not effective at determining if the random curves are an SLE. Tests that involve the independence of the increments of Brownian motion are much more effective. We also study the zipper algorithm for numerically computing the driving function of a simple curve. We give an implementation of this algorithm which runs in a time O(N 1.35) rather than the usual O(N 2), where N is the number of points on the curve.

AB - We simulate several models of random curves in the half plane and numerically compute the stochastic driving processes that produce the curves through the Loewner equation. Our models include models whose scaling limit is the Schramm-Loewner evolution (SLE) and models for which it is not. We study several tests of whether the driving process is Brownian motion, as it is for SLE. We find that testing only the normality of the process at a fixed time is not effective at determining if the random curves are an SLE. Tests that involve the independence of the increments of Brownian motion are much more effective. We also study the zipper algorithm for numerically computing the driving function of a simple curve. We give an implementation of this algorithm which runs in a time O(N 1.35) rather than the usual O(N 2), where N is the number of points on the curve.

KW - Loewner equation

KW - Random curves

KW - SLE

KW - Zipper algorithm

UR - http://www.scopus.com/inward/record.url?scp=43049170359&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=43049170359&partnerID=8YFLogxK

U2 - 10.1007/s10955-008-9535-x

DO - 10.1007/s10955-008-9535-x

M3 - Article

AN - SCOPUS:43049170359

VL - 131

SP - 803

EP - 819

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 5

ER -