### Abstract

Let D be a domain in the plane containing the origin. We are interested in the ensemble of self-avoiding walks (SAWs) in D which start at the origin and end on the boundary of the domain. We introduce an ensemble of SAWs that we expect to have the same scaling limit. The advantage of our ensemble is that it can be simulated using the pivot algorithm. Our ensemble makes it possible to accurately study Schramm-Loewner evolution (SLE) predictions for the SAW in bounded simply connected domains. One such prediction is the distribution along the boundary of the endpoint of the SAW. We use the pivot algorithm to simulate our ensemble and study this density. In particular the lattice effects in this density that persist in the scaling limit are seen to be given by a purely local function.

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

Article number | 095219 |

Journal | Journal of Mathematical Physics |

Volume | 53 |

Issue number | 9 |

DOIs | |

State | Published - Sep 28 2012 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

**Simulating self-avoiding walks in bounded domains.** / Kennedy, Thomas G.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 53, no. 9, 095219. https://doi.org/10.1063/1.4749392

}

TY - JOUR

T1 - Simulating self-avoiding walks in bounded domains

AU - Kennedy, Thomas G

PY - 2012/9/28

Y1 - 2012/9/28

N2 - Let D be a domain in the plane containing the origin. We are interested in the ensemble of self-avoiding walks (SAWs) in D which start at the origin and end on the boundary of the domain. We introduce an ensemble of SAWs that we expect to have the same scaling limit. The advantage of our ensemble is that it can be simulated using the pivot algorithm. Our ensemble makes it possible to accurately study Schramm-Loewner evolution (SLE) predictions for the SAW in bounded simply connected domains. One such prediction is the distribution along the boundary of the endpoint of the SAW. We use the pivot algorithm to simulate our ensemble and study this density. In particular the lattice effects in this density that persist in the scaling limit are seen to be given by a purely local function.

AB - Let D be a domain in the plane containing the origin. We are interested in the ensemble of self-avoiding walks (SAWs) in D which start at the origin and end on the boundary of the domain. We introduce an ensemble of SAWs that we expect to have the same scaling limit. The advantage of our ensemble is that it can be simulated using the pivot algorithm. Our ensemble makes it possible to accurately study Schramm-Loewner evolution (SLE) predictions for the SAW in bounded simply connected domains. One such prediction is the distribution along the boundary of the endpoint of the SAW. We use the pivot algorithm to simulate our ensemble and study this density. In particular the lattice effects in this density that persist in the scaling limit are seen to be given by a purely local function.

UR - http://www.scopus.com/inward/record.url?scp=84867136803&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867136803&partnerID=8YFLogxK

U2 - 10.1063/1.4749392

DO - 10.1063/1.4749392

M3 - Article

VL - 53

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 9

M1 - 095219

ER -