### Abstract

Let ζ_{l} be the critical exponent associated with the probability that l independent N-step ordinary random walks, starting at nearby points, are mutually avoiding. Using Monte Carlo methods combined with a maximum-likelihood data analysis, we find that in two dimensions ζ_{2}=0.6240±0.0005±0.0011 and ζ_{3}=1.4575±0.0030±0.0052, where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second error bar represents statistical error (classical 95% confidence limits). These results are in good agreement with the conformal-invariance predictions ζ_{2}=5/8 and ζ_{3}=35/24.

Original language | English (US) |
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Pages (from-to) | 723-748 |

Number of pages | 26 |

Journal | Journal of Statistical Physics |

Volume | 61 |

Issue number | 3-4 |

DOIs | |

State | Published - Nov 1990 |

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### Keywords

- conformal invariance
- maximum-likelihood estimation
- Monte Carlo
- mutually-avoiding walks
- random walk
- self-avoiding walk

### ASJC Scopus subject areas

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

### Cite this

*Journal of Statistical Physics*,

*61*(3-4), 723-748. https://doi.org/10.1007/BF01027299

**High-precision Monte Carlo test of the conformai-invariance predictions for two-dimensional mutually avoiding walks.** / Li, Bin; Sokal, Alan D.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 61, no. 3-4, pp. 723-748. https://doi.org/10.1007/BF01027299

}

TY - JOUR

T1 - High-precision Monte Carlo test of the conformai-invariance predictions for two-dimensional mutually avoiding walks

AU - Li, Bin

AU - Sokal, Alan D.

PY - 1990/11

Y1 - 1990/11

N2 - Let ζl be the critical exponent associated with the probability that l independent N-step ordinary random walks, starting at nearby points, are mutually avoiding. Using Monte Carlo methods combined with a maximum-likelihood data analysis, we find that in two dimensions ζ2=0.6240±0.0005±0.0011 and ζ3=1.4575±0.0030±0.0052, where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second error bar represents statistical error (classical 95% confidence limits). These results are in good agreement with the conformal-invariance predictions ζ2=5/8 and ζ3=35/24.

AB - Let ζl be the critical exponent associated with the probability that l independent N-step ordinary random walks, starting at nearby points, are mutually avoiding. Using Monte Carlo methods combined with a maximum-likelihood data analysis, we find that in two dimensions ζ2=0.6240±0.0005±0.0011 and ζ3=1.4575±0.0030±0.0052, where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second error bar represents statistical error (classical 95% confidence limits). These results are in good agreement with the conformal-invariance predictions ζ2=5/8 and ζ3=35/24.

KW - conformal invariance

KW - maximum-likelihood estimation

KW - Monte Carlo

KW - mutually-avoiding walks

KW - random walk

KW - self-avoiding walk

UR - http://www.scopus.com/inward/record.url?scp=0009452583&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0009452583&partnerID=8YFLogxK

U2 - 10.1007/BF01027299

DO - 10.1007/BF01027299

M3 - Article

VL - 61

SP - 723

EP - 748

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 3-4

ER -