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

Published online by Cambridge University Press:  15 August 2002

Gregory F. Lawler*
Department of Mathematics, Box 90320, Duke University Durham, NC 27708-0320, USA;
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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 nα. 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.

Research Article
© EDP Sciences, SMAI, 1999

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