Abstract
We give a new proof of a result of Rick Kenyon that the probability that an edge in the middle of an $n \times n$ square is used in a loop-erased walk connecting opposite sides is of order $n^{-3/4}$. We, in fact, improve the result by showing that this estimate is correct up to multiplicative constants.
Citation
Gregory Lawler. "The probability that planar loop-erased random walk uses a given edge." Electron. Commun. Probab. 19 1 - 13, 2014. https://doi.org/10.1214/ECP.v19-2908
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