The probability that planar loop-erased random walk uses a given edge

Gregory F. Lawler

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arXiv · 1301.5331

The probability that planar loop-erased random walk uses a given edge

Gregory F. Lawler

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Abstract

We give a new proof of a result of Rick Kenyon that the probability that an edge in the middle of an n x n square is used in a loop-erased walk connecting opposites sides is of order n^{-3/4}. We, in fact, improve the result by showing that this estimate is correct up to multiplicative constants.

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Gregory F. Lawler. 2013-01-22. The probability that planar loop-erased random walk uses a given edge. https://arxiv.org/abs/1301.5331

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