The length of an SLE-Monte Carlo studies

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7 Scopus citations


The scaling limits of a variety of critical two-dimensional lattice models are equal to the Schramm-Loewner evolution (SLE) for a suitable value of the parameter κ. These lattice models have a natural parametrization of their random curves given by the length of the curve. This parametrization (with suitable scaling) should provide a natural parametrization for the curves in the scaling limit. We conjecture that this parametrization is also given by a type of fractal variation along the curve, and present Monte Carlo simulations to support this conjecture. Then we show by simulations that if this fractal variation is used to parametrize the SLE, then the parametrized curves have the same distribution as the curves in the scaling limit of the lattice models with their natural parametrization.

Original languageEnglish (US)
Pages (from-to)1263-1277
Number of pages15
JournalJournal of Statistical Physics
Issue number6
StatePublished - Sep 2007


  • Fractal variation
  • Natural parametrization
  • Schramm-Loewner evolution

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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