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A Lower Bound on the Growth Exponent for Loop-Erased Random Walk in Two Dimensions

Gregory F. Lawler
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Abstract

The growth exponent $α$ for loop-erased or Laplacian random walk on the integer lattice is defined by saying that the expected time to reach the sphere of radius $n$ is of order $n^α$. We prove that in two dimensions, the growth exponent is strictly greater than one. The proof uses a known estimate on the third moment of the escape probability and an improvement on the discrete Beurling projection theorem.

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Gregory F. Lawler. 1998-03-10. A Lower Bound on the Growth Exponent for Loop-Erased Random Walk in Two Dimensions. https://arxiv.org/abs/math/9803034

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