On the scaling limit of loop-erased random walk excursion |
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Authors: | Fredrik Johansson Viklund |
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Institution: | 1. Department of Mathematics, Columbia University, New York, NY, U.S.A.
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Abstract: | We use the known convergence of loop-erased random walk to radial SLE(2) to give a new proof that the scaling limit of loop-erased random walk excursion in the upper half-plane is chordal SLE(2). Our proof relies on a version of Wilson’s algorithm for weighted graphs which is used together with a Beurling-type estimate for random walk excursion. We also establish and use the convergence of the radial SLE path to the chordal SLE path as the bulk point tends to a boundary point. In the final section we sketch how to extend our results to more general simply connected domains. |
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