Continuous LERW Started from Interior Points

Mathematics – Probability

Scientific paper

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55 pages

Scientific paper

We use the whole-plane Loewner equation to define a family of continuous LERW
in finitely connected domains that are started from interior points. These
continuous LERW satisfy conformal invariance, preserve some continuous local
martingales, and are the scaling limits of the corresponding discrete LERW on
the discrete approximation of the domains.

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