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Scaling limit of the probability that loop-erased random walk uses a given edge

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Random Geometry

Co-authors: Christian Benes (CUNY), Greg Lawler (University of Chicago)

I will discuss a proof of the following result: The probability that a loop-erased random walk (LERW) uses a given edge in the interior of a lattice approximation of a simply connected domain converges in the scaling limit to a constant times the SLE Green’s function, an explicit conformally covariant quantity. I will also indicate how this result is related to convergence of LERW to SLE the natural parameterization.

This is based on joint work with Christian Benes and Greg Lawler and work in progress with Greg Lawler.

This talk is part of the Isaac Newton Institute Seminar Series series.

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