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

Gregory F. Lawler — 2010

ESAIM: Probability and Statistics

The growth exponent 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 is of order . 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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