The Length of an SLE - Monte Carlo Studies
arXiv:math/0612609 · doi:10.1007/s10955-007-9375-0
Abstract
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 kappa. 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.
18 pages, 10 figures. Version 2 replaced the use of "nu" for the "growth exponent" by 1/d_H, where d_H is the Hausdorff dimension. Various minor errors were also corrected
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- Theta-point polymers in the plane and Schramm-Loewner evolution
- Whole-plane self-avoiding walks and radial Schramm-Loewner evolution: a numerical study
- Stochastic Loewner Evolution