A natural parametrization for the Schramm-Loewner evolution
The Schramm-Loewner evolution (SLE) is a model which has been proposed to picture the conformal invariance in the scaling limit of some measures on paths, or clusters on planar lattices, which occur in statistical mechanics. The main purpose of the paper is to propose a Markovian parametrization for this SLE, and to this end the authors derive a Doob-Meyer decomposition for submartingales satisfying a second moment bound. This unique parametrization is referred to as natural to emphasize the analogy with the natural parametrization of smooth curves and the main results are stated in terms of martingales and asymptotic limits.
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