Chordal SLE is defined on any simply connected domain with two marked boundary points by applying a conformal map from the upper half-plane. Its law is independent of the chosen map, up to a deterministic change of parameterization.
The locality property says that an SLE does not detect a hull lying away from its starting point until the curve reaches that hull. Among chordal Schramm-Loewner evolutions, this property holds for .
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