Basic properties of the natural parametrization for the Schramm-Loewner evolution

Details Basic properties of the natural parametrization for the Schramm-Loewner evolution Basic properties of the natural parametrization for the Schramm-Loewner evolution

2012-03-15

arxiv.org/abs/1203.3259v1

Mathematics

Probability

53 pages

Scientific paper

The natural paramterization or length for the Schramm-Loewner evolution (SLE) is the candidate for the scaling limit of the length of discrete curves for kappa < 8. We improve the proof of the existence of the parametrization and use this to establish some new results. In particular, we show that the natural parametrization is independent of domain and it is Holder continuous with respect to the capacity parametrization. We also give up to constants bounds for the two-point Green's function.

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