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loop-erased walk

ESAIM: Probability and Statistics (1)

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A Lower Bound on the Growth Exponent for Loop-Erased Random Walk in Two Dimensions
Gregory F. Lawler
Journal:

ESAIM: Probability and Statistics / Volume 3 / 1999

Published online by Cambridge University Press:

15 August 2002, pp. 1-21

Print publication:

1999
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The growth exponent α for loop-erased or Laplacian random walkon the integer lattice is defined by saying that the expected time toreach the sphere of radius n is of order nα . We prove thatin two dimensions, the growth exponent is strictly greater than one.The proof uses a known estimate on the third moment of the escapeprobability and an improvement on the discrete Beurling projection theorem.