arXiv math/06126092006-12math.PRmath-phmath.MP

The Length of an SLE - Monte Carlo Studies

Tom Kennedy

备注：: 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
发表信息：: J. Statist. Phys. 128 (2007), 1263-1277
DOI：: 10.1007/s10955-007-9375-0

英文摘要：

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.

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