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

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dc.creatorLawler, Gregory F.
dc.date1998-03-10
dc.date.accessioned2026-07-07T05:24:03Z
dc.date.available2026-07-07T05:24:03Z
dc.descriptionThe 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.
dc.identifierhttps://arxiv.org/abs/math/9803034
dc.identifierhttp://arxiv.org/abs/math/9803034
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76683
dc.subjectProbability
dc.subject60J15
dc.titleA Lower Bound on the Growth Exponent for Loop-Erased Random Walk in Two Dimensions
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